In this work, we propose and investigate a delay cell population model of hepatitis C virus (HCV) infection with cellular proliferation, absorption effect and a nonlinear incidence function. First of all, after having shown the existence of the local solutions of our model, we show the existence of the global solutions and positivity. Moreover, we determine the uninfected equilibrium point and the basic reproduction rate R0, which is a threshold number in mathematical epidemiology. After showing the existence and uniqueness of the infected equilibrium point, we proceed to the study of the local and global stability of this equilibrium. We show that if R0 < 1, the uninfected equilibrium point is globally asymptotically stable, which means that the disease will disappear and if R0 > 1, we have a unique infected equilibrium that is globally asymptotically stable under some conditions. Finally, we perform some numerical simulations to illustrate the obtained theoretical results.
{"title":"Global stability of a delay HCV dynamics model with cellular proliferation","authors":"Alexis Nangue, Armel Willy Fokam Tacteu, Ayouba Guedlai","doi":"10.5206/mase/14918","DOIUrl":"https://doi.org/10.5206/mase/14918","url":null,"abstract":"In this work, we propose and investigate a delay cell population model of hepatitis C virus (HCV) infection with cellular proliferation, absorption effect and a nonlinear incidence function. First of all, after having shown the existence of the local solutions of our model, we show the existence of the global solutions and positivity. Moreover, we determine the uninfected equilibrium point and the basic reproduction rate R0, which is a threshold number in mathematical epidemiology. After showing the existence and uniqueness of the infected equilibrium point, we proceed to the study of the local and global stability of this equilibrium. We show that if R0 < 1, the uninfected equilibrium point is globally asymptotically stable, which means that the disease will disappear and if R0 > 1, we have a unique infected equilibrium that is globally asymptotically stable under some conditions. Finally, we perform some numerical simulations to illustrate the obtained theoretical results.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45026529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Second-order macroscopic traffic models are characterized by a continuity equation and an acceleration equation. Convection, anticipation, relaxation, diffusion, and viscosity are the predominant features of the different classes of the acceleration equation. As a unique approach, this paper presents a new macro-model that accounts for all these dynamic speed quantities. This is done to determine the collective role of these traffic quantities in macroscopic modeling. The proposed model is solved numerically to explain some phenomena of a multilane traffic flow. It also includes a linear stability analysis. Furthermore, the evolution of speed and density wave profiles are presented under the perturbation of some parameters.
{"title":"Macroscopic Analysis Of The Viscous-Diffusive Traffic Flow Model","authors":"Gabriel Obed Fosu, A. Adu-Sackey, J. Ackora-Prah","doi":"10.5206/mase/14626","DOIUrl":"https://doi.org/10.5206/mase/14626","url":null,"abstract":"Second-order macroscopic traffic models are characterized by a continuity equation and an acceleration equation. Convection, anticipation, relaxation, diffusion, and viscosity are the predominant features of the different classes of the acceleration equation. As a unique approach, this paper presents a new macro-model that accounts for all these dynamic speed quantities. This is done to determine the collective role of these traffic quantities in macroscopic modeling. The proposed model is solved numerically to explain some phenomena of a multilane traffic flow. It also includes a linear stability analysis. Furthermore, the evolution of speed and density wave profiles are presented under the perturbation of some parameters.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42538647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Ghasemi, Viktoria Freingruber, C. Kuttler, H. Eberl
We extend a previously presented mesoscopic (i.e. colony scale) mathematical model of the reaction of bacterial biofilms to antibiotics. In that earlier model, exposure to antibiotics evokes two responses: inactivation as the antibiotics kill the bacteria, and inducing a quorum sensing based stress response mechanism upon exposure to small sublethal dosages. To this model we add now quorum quenching as an adjuvant to antibiotic therapy. Quorum quenchers are modeled like enzymes that degrade the quorum sensing signal concentration. The resulting model is a quasilinear system of seven reaction-diffusion equations for the dependent variables volume fractions of upregulated (protected), downregulated (unprotected) and inert (inactive) biomass [particulate substances], and for concentrations of a growth promoting nutrient, antibiotics, quorum sensing signal, and quorum quenchers [dissolved substances]. The biomass fractions are subject to two nonlinear diffusion effects: (i) degeneracy, as in the porous medium equation, where biomass vanishes, and (ii) a super-diffusion singularity where as it attains its theoretically possible maximum. We study this model in numerical simulations. Our simulations suggest that for maximum efficacy quorum quenchers should be applied early on before quorum sensing induction in the biofilm can take place, and that an antibiotic strategy that by itself might not be successful can be notably improved upon if paired with quorum quenchers as an adjuvant.
{"title":"A mathematical model of quorum quenching in biofilm colonies and its potential role as an adjuvant for antibiotic treatment","authors":"M. Ghasemi, Viktoria Freingruber, C. Kuttler, H. Eberl","doi":"10.5206/mase/14612","DOIUrl":"https://doi.org/10.5206/mase/14612","url":null,"abstract":"We extend a previously presented mesoscopic (i.e. colony scale) mathematical model of the reaction of bacterial biofilms to antibiotics. In that earlier model, exposure to antibiotics evokes two responses: inactivation as the antibiotics kill the bacteria, and inducing a quorum sensing based stress response mechanism upon exposure to small sublethal dosages. To this model we add now quorum quenching as an adjuvant to antibiotic therapy. Quorum quenchers are modeled like enzymes that degrade the quorum sensing signal concentration. The resulting model is a quasilinear system of seven reaction-diffusion equations for the dependent variables volume fractions of upregulated (protected), downregulated (unprotected) and inert (inactive) biomass [particulate substances], and for concentrations of a growth promoting nutrient, antibiotics, quorum sensing signal, and quorum quenchers [dissolved substances]. The biomass fractions are subject to two nonlinear diffusion effects: (i) degeneracy, as in the porous medium equation, where biomass vanishes, and (ii) a super-diffusion singularity where as it attains its theoretically possible maximum. We study this model in numerical simulations. Our simulations suggest that for maximum efficacy quorum quenchers should be applied early on before quorum sensing induction in the biofilm can take place, and that an antibiotic strategy that by itself might not be successful can be notably improved upon if paired with quorum quenchers as an adjuvant.\u0000 ","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43112018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexis Nangue, Paulin Tiomo Lemofouet, Simon Ndouvatama, Kengne Emmanuel
In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.
{"title":"Global Analysis of a generalized viral infection temporal model with cell-to-cell transmission and absorption effect under therapy","authors":"Alexis Nangue, Paulin Tiomo Lemofouet, Simon Ndouvatama, Kengne Emmanuel","doi":"10.5206/mase/14663","DOIUrl":"https://doi.org/10.5206/mase/14663","url":null,"abstract":"In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42701270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gabriel Obed Fosu, J. Opong, B. E. Owusu, S. Naandam
The continual wearing of road surfaces results to crack and holes called potholes. These road surface irregularities often elongate travel time. In this paper, a second-order macroscopic traffic model is therefore proposed to account for these road surface irregularities that affect the smooth flow of vehicular traffic. Though potholes do vary in shape and size, for simplicity the paper assumes that all potholes have conic resemblances. The impact of different sized potholes on driving is experimented using fundamental diagrams. Besides, the width of these holes, driver reaction time amid these irregularities also determine the intensity of the flow rate and vehicular speed. Moreover, a local cluster analysis is performed to determine the effect of a small disturbance on flow. The results revealed that the magnitude of amplification on a road surface with larger cracks is not as severe as roads with smaller size holes, except at minimal and jam density where all amplifications quickly fade out.
{"title":"Modeling road surface potholes within the macroscopic flow framework","authors":"Gabriel Obed Fosu, J. Opong, B. E. Owusu, S. Naandam","doi":"10.5206/mase/14625","DOIUrl":"https://doi.org/10.5206/mase/14625","url":null,"abstract":"The continual wearing of road surfaces results to crack and holes called potholes. These road surface irregularities often elongate travel time. In this paper, a second-order macroscopic traffic model is therefore proposed to account for these road surface irregularities that affect the smooth flow of vehicular traffic. Though potholes do vary in shape and size, for simplicity the paper assumes that all potholes have conic resemblances. The impact of different sized potholes on driving is experimented using fundamental diagrams. Besides, the width of these holes, driver reaction time amid these irregularities also determine the intensity of the flow rate and vehicular speed. Moreover, a local cluster analysis is performed to determine the effect of a small disturbance on flow. The results revealed that the magnitude of amplification on a road surface with larger cracks is not as severe as roads with smaller size holes, except at minimal and jam density where all amplifications quickly fade out.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-30Epub Date: 2022-02-20DOI: 10.5206/mase/14537
Ben Patterson, Jin Wang
We introduce two mathematical models based on systems of differential equations to investigate the relationship between the latency period and the transmission dynamics of COVID-19. We analyze the equilibrium and stability properties of these models, and perform an asymptotic study in terms of small and large latency periods. We fit the models to the COVID-19 data in the U.S. state of Tennessee. Our numerical results demonstrate the impact of the latency period on the dynamical behaviors of the solutions, on the value of the basic reproduction numbers, and on the accuracy of the model predictions.
{"title":"HOW DOES THE LATENCY PERIOD IMPACT THE MODELING OF COVID-19 TRANSMISSION DYNAMICS?","authors":"Ben Patterson, Jin Wang","doi":"10.5206/mase/14537","DOIUrl":"https://doi.org/10.5206/mase/14537","url":null,"abstract":"<p><p>We introduce two mathematical models based on systems of differential equations to investigate the relationship between the latency period and the transmission dynamics of COVID-19. We analyze the equilibrium and stability properties of these models, and perform an asymptotic study in terms of small and large latency periods. We fit the models to the COVID-19 data in the U.S. state of Tennessee. Our numerical results demonstrate the impact of the latency period on the dynamical behaviors of the solutions, on the value of the basic reproduction numbers, and on the accuracy of the model predictions.</p>","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9302022/pdf/nihms-1821943.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40534023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper analyses a discrete predator-prey system with fear effect and density dependent birth rate of the prey species. The fixed points of the system are determined and their stability is examined. The criterion for Neimark-Sacker bifurcation and flip bifurcation is developed. The chaotic orbit at an unstable fixed point can be stabilized by applying the state feedback control method. Numerically, we illustrate our analytical findings and observe the complex behaviour of the system that leads to stable state to chaotic one.
{"title":"Dynamics of discrete predator- prey system with fear effect and density dependent birth rate of the prey species","authors":"D. Mukherjee","doi":"10.5206/mase/14496","DOIUrl":"https://doi.org/10.5206/mase/14496","url":null,"abstract":"This paper analyses a discrete predator-prey system with fear effect and density dependent birth rate of the prey species. The fixed points of the system are determined and their stability is examined. The criterion for Neimark-Sacker bifurcation and flip bifurcation is developed. The chaotic orbit at an unstable fixed point can be stabilized by applying the state feedback control method. Numerically, we illustrate our analytical findings and observe the complex behaviour of the system that leads to stable state to chaotic one.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47290997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ecological stoichiometry provides a multi-scale approach to study macroscopic phenomena via microscopic lens. A stoichiometric producer-grazer model with maturation delay is proposed and studied in this paper. The interaction between stoichiometry and delay is novel and leads to more interesting insights beyond classical delay-driven periodic solutions. For example, the period doubling route to chaos can occur as the minimal phosphorous:carbon ratio in producer decreases. Mathematically, we establish the conditions for the existence and stability of positive equilibria, and study the occurrence of Hopf bifurcation at positive equilibria. Analytic results show that delay can change the number and stability of positive equilibria through transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, and it further determines the grazer's extinction. Our model with a small delay behaves like LKE model in terms of light intensity, and Rosenzweig's paradox of enrichment exists in a suitable light intensity. We plot bifurcation diagrams and show rich dynamics driven by delay, light intensity, phosphorous availability, and conversion efficiency, including that a large delay can drive the grazer to go extinct in an intermediate light intensity that is favorable for the survival of the grazer when there is no delay; a limit cycle can appear, then disappear as the delay increases; given the same initial condition, solutions with different delay values can tend to different attractors.
{"title":"Dynamics of a stoichiometric producer-grazer model with maturation delay","authors":"Hua Zhang, Hao Wang, Ben Niu","doi":"10.5206/mase/14332","DOIUrl":"https://doi.org/10.5206/mase/14332","url":null,"abstract":"Ecological stoichiometry provides a multi-scale approach to study macroscopic phenomena via microscopic lens. A stoichiometric producer-grazer model with maturation delay is proposed and studied in this paper. The interaction between stoichiometry and delay is novel and leads to more interesting insights beyond classical delay-driven periodic solutions. For example, the period doubling route to chaos can occur as the minimal phosphorous:carbon ratio in producer decreases. Mathematically, we establish the conditions for the existence and stability of positive equilibria, and study the occurrence of Hopf bifurcation at positive equilibria. Analytic results show that delay can change the number and stability of positive equilibria through transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, and it further determines the grazer's extinction. Our model with a small delay behaves like LKE model in terms of light intensity, and Rosenzweig's paradox of enrichment exists in a suitable light intensity. We plot bifurcation diagrams and show rich dynamics driven by delay, light intensity, phosphorous availability, and conversion efficiency, including that a large delay can drive the grazer to go extinct in an intermediate light intensity that is favorable for the survival of the grazer when there is no delay; a limit cycle can appear, then disappear as the delay increases; given the same initial condition, solutions with different delay values can tend to different attractors.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42067231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ant Colony Optimization (ACO) metaheuristic is a multi-agent system in which the behaviour of each ant is inspired by the foraging behaviour of real ants to solve optimization problem. Set Covering Problems (SCP), on the other hand, deal with maximizing the coverage of every subset while the weight nodes used must be minimized. In this paper, ACO was adapted and used to solve a case of Set Covering Problem. The adapted ACO for solving the SCP was implemented as a computer program using SciLab 5.4.1. The problem of determining the optimal location of Wi-Fi Access Points using the 802.11n protocol in the UP Los Banos Math Building was solved using this metaheuristic. Results show that in order to have 100% coverage of the MB, 7 access points are required. Methodology of the study can be adapted and results of the study can be used by decision makers on related optimization problems.
蚁群优化（ACO）元启发式是一个多智能体系统，其中每个蚂蚁的行为都受到真实蚂蚁觅食行为的启发，以解决优化问题。另一方面，集覆盖问题（SCP）处理的是最大化每个子集的覆盖，而使用的权重节点必须最小化。本文将ACO方法应用于一个集覆盖问题的求解。使用SciLab 5.4.1将用于解决SCP的自适应ACO实现为计算机程序。使用这种元启发式方法解决了在UP Los Banos数学大楼中使用802.11n协议确定Wi-Fi接入点的最佳位置的问题。结果显示，为了实现MB的100%覆盖，需要7个接入点。研究方法可以进行调整，决策者可以将研究结果用于相关的优化问题。
{"title":"Application of ant colony optimization metaheuristic on set covering problems","authors":"C. A. Buhat, Jerson Ken Villamin, G. Cuaresma","doi":"10.5206/mase/14018","DOIUrl":"https://doi.org/10.5206/mase/14018","url":null,"abstract":"Ant Colony Optimization (ACO) metaheuristic is a multi-agent system in which the behaviour of each ant is inspired by the foraging behaviour of real ants to solve optimization problem. Set Covering Problems (SCP), on the other hand, deal with maximizing the coverage of every subset while the weight nodes used must be minimized. In this paper, ACO was adapted and used to solve a case of Set Covering Problem. The adapted ACO for solving the SCP was implemented as a computer program using SciLab 5.4.1. The problem of determining the optimal location of Wi-Fi Access Points using the 802.11n protocol in the UP Los Banos Math Building was solved using this metaheuristic. Results show that in order to have 100% coverage of the MB, 7 access points are required. Methodology of the study can be adapted and results of the study can be used by decision makers on related optimization problems.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43143732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy.
{"title":"On approximating initial data in some linear evolutionary equations involving fraction Laplacian","authors":"R. Karki","doi":"10.5206/mase/13511","DOIUrl":"https://doi.org/10.5206/mase/13511","url":null,"abstract":"We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy. ","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43896471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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