Rogério M. Saldanha da Gama, José Julio Pedrosa Filho, Rogério Pazetto S. da Gama, Daniel Cunha da Silva, Carlos Henrique Alexandrino, Maria Laura Martins-Costa
This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated–unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem’s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm’s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm’s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic.
{"title":"Numerical Simulation of Constrained Flows through Porous Media Employing Glimm’s Scheme","authors":"Rogério M. Saldanha da Gama, José Julio Pedrosa Filho, Rogério Pazetto S. da Gama, Daniel Cunha da Silva, Carlos Henrique Alexandrino, Maria Laura Martins-Costa","doi":"10.3390/axioms12111023","DOIUrl":"https://doi.org/10.3390/axioms12111023","url":null,"abstract":"This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated–unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem’s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm’s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm’s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136023068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret–Frenet frame, the surface pencil couple can be expressed as linear combinations of the components of the local frames in Galilean 3-space G3. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand couple to be the principal curves on these surfaces are derived in our approach. Moreover, the necessary and sufficient condition for the given Bertrand couple to satisfy the principal curves and the geodesic requirements are also analyzed. As implementations of our main consequences, we expound upon some models to confirm the method.
{"title":"Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space","authors":"Nadia Alluhaibi, Rashad A. Abdel-Baky","doi":"10.3390/axioms12111022","DOIUrl":"https://doi.org/10.3390/axioms12111022","url":null,"abstract":"A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret–Frenet frame, the surface pencil couple can be expressed as linear combinations of the components of the local frames in Galilean 3-space G3. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand couple to be the principal curves on these surfaces are derived in our approach. Moreover, the necessary and sufficient condition for the given Bertrand couple to satisfy the principal curves and the geodesic requirements are also analyzed. As implementations of our main consequences, we expound upon some models to confirm the method.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136023070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Every red–blue coloring of the edges of a graph G results in a sequence G1, G2, …, Gℓ of pairwise edge-disjoint monochromatic subgraphs Gi (1≤i≤ℓ) of size i, such that Gi is isomorphic to a subgraph of Gi+1 for 1≤i≤ℓ−1. Such a sequence is called a Ramsey chain in G, and ARc(G) is the maximum length of a Ramsey chain in G, with respect to a red–blue coloring c. The Ramsey index AR(G) of G is the minimum value of ARc(G) among all the red–blue colorings c of G. If G has size m, then k+12≤m
对图G的每条边进行红蓝着色，得到大小为i的对边不相交的单色子图Gi(1≤i≤r)的序列G1, G2，…，G，使得Gi在1≤i≤r−1时与Gi+1的子图同构。这样的序列称为拉姆齐链G,和弧(G)的最大长度是拉姆齐连锁G,对红蓝着色c。拉姆齐指数基于“增大化现实”技术(G)的最小值是G的弧(G)在所有G .如果G大小的红蓝色素c m, k + 12≤m<一些正整数k + 22 k。它已经表明,有无限类的图表,这样每一个图G的大小m S,基于“增大化现实”技术(G) = k当且仅当k + 12≤m< k + 22。其中两个类是匹配大小为m的mK2和路径Pm+1。它们都是线性森林的子类(其中每个组件都是路径)。证明了如果F是任意大小为m且k+12<m<k+22的线性森林，则AR(F)=k。更进一步，如果F是一个大小为k+12的线性森林，其中k≥4，最多有k−12个分量，则AR(F)=k，而对于k−12<t<k+12的每一个整数t，存在一个大小为k+12，有t个分量的线性森林F，使得AR(F)=k−1。
{"title":"Ramsey Chains in Linear Forests","authors":"Gary Chartrand, Ritabrato Chatterjee, Ping Zhang","doi":"10.3390/axioms12111019","DOIUrl":"https://doi.org/10.3390/axioms12111019","url":null,"abstract":"Every red–blue coloring of the edges of a graph G results in a sequence G1, G2, …, Gℓ of pairwise edge-disjoint monochromatic subgraphs Gi (1≤i≤ℓ) of size i, such that Gi is isomorphic to a subgraph of Gi+1 for 1≤i≤ℓ−1. Such a sequence is called a Ramsey chain in G, and ARc(G) is the maximum length of a Ramsey chain in G, with respect to a red–blue coloring c. The Ramsey index AR(G) of G is the minimum value of ARc(G) among all the red–blue colorings c of G. If G has size m, then k+12≤m<k+22 for some positive integer k. It has been shown that there are infinite classes S of graphs, such that for every graph G of size m in S, AR(G)=k if and only if k+12≤m<k+22. Two of these classes are the matchings mK2 and paths Pm+1 of size m. These are both subclasses of linear forests (a forest of which each of the components is a path). It is shown that if F is any linear forest of size m with k+12<m<k+22, then AR(F)=k. Furthermore, if F is a linear forest of size k+12, where k≥4, that has at most k−12 components, then AR(F)=k, while for each integer t with k−12<t<k+12 there is a linear forest F of size k+12 with t components, such that AR(F)=k−1.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"1187 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136136034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Akbar Azam, Maliha Rashid, Amna Kalsoom, Faryad Ali
This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.
{"title":"Fixed-Point Convergence of Multi-Valued Non-Expansive Mappings with Applications","authors":"Akbar Azam, Maliha Rashid, Amna Kalsoom, Faryad Ali","doi":"10.3390/axioms12111020","DOIUrl":"https://doi.org/10.3390/axioms12111020","url":null,"abstract":"This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136135283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this article is to introduce and study certain families of normalized certain functions with symmetric points connected to Gegenbauer polynomials. Moreover, we determine the upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3| and resolve the Fekete–Szegöproblem for these functions. In addition, we establish links to a few of the earlier discovered outcomes.
{"title":"Coefficient Bounds and Fekete–Szegö Inequalities for a Two Families of Bi-Univalent Functions Related to Gegenbauer Polynomials","authors":"Yahya Almalki, Abbas Kareem Wanas, Timilehin Gideon Shaba, Alina Alb Lupaş, Mohamed Abdalla","doi":"10.3390/axioms12111018","DOIUrl":"https://doi.org/10.3390/axioms12111018","url":null,"abstract":"The purpose of this article is to introduce and study certain families of normalized certain functions with symmetric points connected to Gegenbauer polynomials. Moreover, we determine the upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3| and resolve the Fekete–Szegöproblem for these functions. In addition, we establish links to a few of the earlier discovered outcomes.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"19 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136158101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the intensification of global competition and the increasing awareness of reducing energy consumption, sustainable supplier selection is crucial for establishing a solid cooperative relationship in sustainable supply chain management. This paper proposes a new framework that considers both the effective expression of uncertain information and the objective weights of decision makers to select sustainable suppliers. We first apply an interval-valued intuitionistic fuzzy set to express the information of decision makers. Moreover, this paper applies a plant growth simulation algorithm to aggregate decision makers’ information. Next, we adopt the similarity measure method to derive the target weight of each decision maker. Then, we apply the score function to rank the candidate sustainable suppliers. Finally, two practical cases are presented to verify the effectiveness of the proposed framework. The outcomes and comparative discussion show that the developed framework is efficient for sustainable supplier selection. Therefore, the proposed framework can be used to establish a solid cooperative relationship in the process of sustainable supply chain management.
{"title":"A New Framework for Sustainable Supplier Selection Based on a Plant Growth Simulation Algorithm","authors":"Jing Li, Weizhong Wang","doi":"10.3390/axioms12111017","DOIUrl":"https://doi.org/10.3390/axioms12111017","url":null,"abstract":"With the intensification of global competition and the increasing awareness of reducing energy consumption, sustainable supplier selection is crucial for establishing a solid cooperative relationship in sustainable supply chain management. This paper proposes a new framework that considers both the effective expression of uncertain information and the objective weights of decision makers to select sustainable suppliers. We first apply an interval-valued intuitionistic fuzzy set to express the information of decision makers. Moreover, this paper applies a plant growth simulation algorithm to aggregate decision makers’ information. Next, we adopt the similarity measure method to derive the target weight of each decision maker. Then, we apply the score function to rank the candidate sustainable suppliers. Finally, two practical cases are presented to verify the effectiveness of the proposed framework. The outcomes and comparative discussion show that the developed framework is efficient for sustainable supplier selection. Therefore, the proposed framework can be used to establish a solid cooperative relationship in the process of sustainable supply chain management.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136231919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ekaterina A. Titova, Peter K. Galenko, Margarita A. Nikishina, Liubov V. Toropova, Dmitri V. Alexandrov
The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a constant crystallization velocity, which is the sum of the steady-state and translational velocities. The dendrite tips in the form of a parabola, paraboloid, and elliptic paraboloid are considered. Taking this solution into account, we obtain the modified boundary integral equation describing the evolution of the patterns and dendrites in undercooled binary melts. Our analysis shows that dendritic tips always evolve in a steady-state manner when considering a kinetically controlled crystallization scenario. The steady-state growth velocity as a factor that is dependent on the melt undercooling, solute concentration, atomic kinetics, and other system parameters is derived. This expression can be used for determining the selection constant of the stable dendrite growth mode in the case of kinetically controlled crystallization.
{"title":"The Boundary Integral Equation for Kinetically Limited Dendrite Growth","authors":"Ekaterina A. Titova, Peter K. Galenko, Margarita A. Nikishina, Liubov V. Toropova, Dmitri V. Alexandrov","doi":"10.3390/axioms12111016","DOIUrl":"https://doi.org/10.3390/axioms12111016","url":null,"abstract":"The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a constant crystallization velocity, which is the sum of the steady-state and translational velocities. The dendrite tips in the form of a parabola, paraboloid, and elliptic paraboloid are considered. Taking this solution into account, we obtain the modified boundary integral equation describing the evolution of the patterns and dendrites in undercooled binary melts. Our analysis shows that dendritic tips always evolve in a steady-state manner when considering a kinetically controlled crystallization scenario. The steady-state growth velocity as a factor that is dependent on the melt undercooling, solute concentration, atomic kinetics, and other system parameters is derived. This expression can be used for determining the selection constant of the stable dendrite growth mode in the case of kinetically controlled crystallization.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"31 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136231915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.
{"title":"Congruence Representations via Soft Ideals in Soft Topological Spaces","authors":"Zanyar A. Ameen, Mesfer H. Alqahtani","doi":"10.3390/axioms12111015","DOIUrl":"https://doi.org/10.3390/axioms12111015","url":null,"abstract":"This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"302 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136231787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of finding the optimal open-loop control for discrete-time stochastic dynamical systems is considered. It is assumed that the initial conditions and external influences are random. The average value of the Bolza functional defined on individual trajectories is minimized. It is proposed to solve the problem by means of classical and modified migrating optimization algorithms. The modification of the migrating algorithm consists of cloning the members of the initial population and choosing different strategies of migratory behavior for the main population and for populations formed by clones. At the final stage of the search for an extremum, an intensively clarifying migration cycle is implemented with the participation of three leaders of the populations participating in the search process. Problems of optimal control of bundles of trajectories of deterministic discrete dynamical systems, as well as individual trajectories, are considered as special cases. Seven model examples illustrating the performance of the proposed approach are solved.
{"title":"Application of Migrating Optimization Algorithms in Problems of Optimal Control of Discrete-Time Stochastic Dynamical Systems","authors":"Andrei Panteleev, Vladislav Rakitianskii","doi":"10.3390/axioms12111014","DOIUrl":"https://doi.org/10.3390/axioms12111014","url":null,"abstract":"The problem of finding the optimal open-loop control for discrete-time stochastic dynamical systems is considered. It is assumed that the initial conditions and external influences are random. The average value of the Bolza functional defined on individual trajectories is minimized. It is proposed to solve the problem by means of classical and modified migrating optimization algorithms. The modification of the migrating algorithm consists of cloning the members of the initial population and choosing different strategies of migratory behavior for the main population and for populations formed by clones. At the final stage of the search for an extremum, an intensively clarifying migration cycle is implemented with the participation of three leaders of the populations participating in the search process. Problems of optimal control of bundles of trajectories of deterministic discrete dynamical systems, as well as individual trajectories, are considered as special cases. Seven model examples illustrating the performance of the proposed approach are solved.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"281 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vladimir E. Fedorov, Marina V. Plekhanova, Daria V. Melekhina
Nonlinear identification problems for evolution differential equations, solved with respect to the highest-order Dzhrbashyan–Nersesyan fractional derivative, are studied. An equation of the considered class contains a linear unbounded operator, which generates analytic resolving families for the corresponding linear homogeneous equation, and a continuous nonlinear operator, which depends on lower-order Dzhrbashyan–Nersesyan derivatives and a depending on time unknown element. The identification problem consists of the equation, Dzhrbashyan–Nersesyan initial value conditions and an abstract overdetermination condition, which is defined by a linear continuous operator. Using the contraction mappings theorem, we prove the unique local solvability of the identification problem. The cases of mild and classical solutions are studied. The obtained abstract results are applied to an investigation of a nonlinear identification problem to a linearized phase field system with time dependent unknown coefficients at Dzhrbashyan–Nersesyan time-derivatives of lower orders.
{"title":"On Local Unique Solvability for a Class of Nonlinear Identification Problems","authors":"Vladimir E. Fedorov, Marina V. Plekhanova, Daria V. Melekhina","doi":"10.3390/axioms12111013","DOIUrl":"https://doi.org/10.3390/axioms12111013","url":null,"abstract":"Nonlinear identification problems for evolution differential equations, solved with respect to the highest-order Dzhrbashyan–Nersesyan fractional derivative, are studied. An equation of the considered class contains a linear unbounded operator, which generates analytic resolving families for the corresponding linear homogeneous equation, and a continuous nonlinear operator, which depends on lower-order Dzhrbashyan–Nersesyan derivatives and a depending on time unknown element. The identification problem consists of the equation, Dzhrbashyan–Nersesyan initial value conditions and an abstract overdetermination condition, which is defined by a linear continuous operator. Using the contraction mappings theorem, we prove the unique local solvability of the identification problem. The cases of mild and classical solutions are studied. The obtained abstract results are applied to an investigation of a nonlinear identification problem to a linearized phase field system with time dependent unknown coefficients at Dzhrbashyan–Nersesyan time-derivatives of lower orders.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136316441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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