Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130411
Joaquim Duran
We study the family of operators associated to the Robin-type problems in a bounded domain and their dependency on the boundary parameter a as it moves along . In this regard, we study the convergence of such operators in a resolvent sense. We also describe the eigenvalues of such operators and show some of their properties, both for all fixed a and as functions of the parameter a. As shall be seen in more detail in the paper [23], the eigenvalues of these operators characterize the positive eigenvalues of quantum dot Dirac operators.
{"title":"The ∂‾-Robin Laplacian","authors":"Joaquim Duran","doi":"10.1016/j.jmaa.2026.130411","DOIUrl":"10.1016/j.jmaa.2026.130411","url":null,"abstract":"<div><div>We study the family of operators <span><math><msub><mrow><mo>{</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></mrow></msub></math></span> associated to the Robin-type problems in a bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi></mtd><mtd><mtext>in </mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mn>2</mn><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mo>∂</mo></mrow><mrow><mover><mrow><mi>z</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mtext>on </mtext><mo>∂</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> and their dependency on the boundary parameter <em>a</em> as it moves along <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></math></span>. In this regard, we study the convergence of such operators in a resolvent sense. We also describe the eigenvalues of such operators and show some of their properties, both for all fixed <em>a</em> and as functions of the parameter <em>a</em>. As shall be seen in more detail in the paper <span><span>[23]</span></span>, the eigenvalues of these operators characterize the positive eigenvalues of quantum dot Dirac operators.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130411"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038209","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130418
M. Efendiev , M. Ôtani , S. Sivaloganathan
In a recent paper, E. Hughes et al. introduced a coupled ODE-PDE model to study the propagation of invasive tree species. These species, often originating from the Pinacea family, have had a demonstrably negative impact on grassland ecosystems worldwide (particularly in regions such as New Zealand, South Africa, and Chile). In this paper, we apply the classical subdifferential operator theory due to H. Brézis [1] to establish existence and uniqueness of solutions to the coupled ODE-PDE model for studying the propagation of invasive tree species in grassland ecosystems. Ensuring precise prediction of invasive tree population behaviour in grasslands is critical for effective invasive species management. To this purpose, we further prove the existence of a unique stationary state and discuss its stability. In this process, -energy method plays a crucial role.
A subsequent study will delve into the long-term dynamics of the model, investigating the existence of travelling wave solutions in unbounded domains.
{"title":"Existence, uniqueness of solutions to a coupled ODE-PDE model of invasive tree species, and stability of steady state solutions","authors":"M. Efendiev , M. Ôtani , S. Sivaloganathan","doi":"10.1016/j.jmaa.2026.130418","DOIUrl":"10.1016/j.jmaa.2026.130418","url":null,"abstract":"<div><div>In a recent paper, E. Hughes et al. introduced a coupled ODE-PDE model to study the propagation of invasive tree species. These species, often originating from the Pinacea family, have had a demonstrably negative impact on grassland ecosystems worldwide (particularly in regions such as New Zealand, South Africa, and Chile). In this paper, we apply the classical subdifferential operator theory due to H. Brézis <span><span>[1]</span></span> to establish existence and uniqueness of solutions to the coupled ODE-PDE model for studying the propagation of invasive tree species in grassland ecosystems. Ensuring precise prediction of invasive tree population behaviour in grasslands is critical for effective invasive species management. To this purpose, we further prove the existence of a unique stationary state and discuss its stability. In this process, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-energy method plays a crucial role.</div><div>A subsequent study will delve into the long-term dynamics of the model, investigating the existence of travelling wave solutions in unbounded domains.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130418"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024438","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130433
Rohit Nageshwar , Tarun Das , Abdul Gaffar Khan
In this paper, we prove that bi-asymptotically c-expansive continuous surjective maps with the shadowing property on compact metric spaces have the two-sided s-limit shadowing property and characterize their entropy in terms of the growth of their periodic orbits. We also show that asymptotically expansive continuous surjective maps with the eventual shadowing property on compact metric spaces have the limit shadowing property. We further introduce the notion of asymptotically expansive points for continuous maps on compact metric spaces and establish that if a continuous map is asymptotically expansive on a neighborhood of a non-isolated, non-periodic, non-wandering, shadowable point of the map, then it has positive topological entropy.
{"title":"On bi-asymptotic c-expansivity and shadowing property","authors":"Rohit Nageshwar , Tarun Das , Abdul Gaffar Khan","doi":"10.1016/j.jmaa.2026.130433","DOIUrl":"10.1016/j.jmaa.2026.130433","url":null,"abstract":"<div><div>In this paper, we prove that bi-asymptotically <em>c</em>-expansive continuous surjective maps with the shadowing property on compact metric spaces have the two-sided <em>s</em>-limit shadowing property and characterize their entropy in terms of the growth of their periodic orbits. We also show that asymptotically expansive continuous surjective maps with the eventual shadowing property on compact metric spaces have the limit shadowing property. We further introduce the notion of asymptotically expansive points for continuous maps on compact metric spaces and establish that if a continuous map is asymptotically expansive on a neighborhood of a non-isolated, non-periodic, non-wandering, shadowable point of the map, then it has positive topological entropy.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130433"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038208","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130413
Dieme P. da Silva , Roger P. de Moura , Gleison N. Santos
The main purpose of this paper is to prove a unique continuation result for n-dimensional Zakharov-Kuznetsov equations, . Our proof relies on complex variable techniques introduced by Bourgain [2]. The Bourgain unique continuation result is here extended for the n-dimensional Zakharov-Kuznetsov equations. As an application we prove the exponential decay of the energy for the n-dimensional Zakharov-Kuznetsov (ZK) equations with localized damping.
{"title":"On the unique continuation and stabilization for the n-dimensional Zakharov-Kuznetsov equation","authors":"Dieme P. da Silva , Roger P. de Moura , Gleison N. Santos","doi":"10.1016/j.jmaa.2026.130413","DOIUrl":"10.1016/j.jmaa.2026.130413","url":null,"abstract":"<div><div>The main purpose of this paper is to prove a unique continuation result for <em>n</em>-dimensional Zakharov-Kuznetsov equations, <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>. Our proof relies on complex variable techniques introduced by Bourgain <span><span>[2]</span></span>. The Bourgain unique continuation result is here extended for the <em>n</em>-dimensional Zakharov-Kuznetsov equations. As an application we prove the exponential decay of the energy for the <em>n</em>-dimensional Zakharov-Kuznetsov (ZK) equations with localized damping.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130413"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978196","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130414
Hui Xu , Xingyu Zhao , Longben Wei
The aim of this paper is to establish two uncertainty principles for the multidimensional Fourier–Bessel transform. The first one is an extension of the Amrein–Berthier theorem, stating that a nonzero function f and its multidimensional Fourier–Bessel transform cannot both have supports of finite measure. The second one is the Logvinenko–Sereda theorem, which provides a quantitative version of the uncertainty principle by showing that a function whose multidimensional Fourier–Bessel transform has bounded support can be controlled by its restriction to any relatively dense subset. Both results extend the corresponding one-dimensional uncertainty principles for the Fourier–Bessel transform to the multidimensional setting.
{"title":"The uncertainty principles for the multidimensional Fourier–Bessel transform","authors":"Hui Xu , Xingyu Zhao , Longben Wei","doi":"10.1016/j.jmaa.2026.130414","DOIUrl":"10.1016/j.jmaa.2026.130414","url":null,"abstract":"<div><div>The aim of this paper is to establish two uncertainty principles for the multidimensional Fourier–Bessel transform. The first one is an extension of the Amrein–Berthier theorem, stating that a nonzero function <em>f</em> and its multidimensional Fourier–Bessel transform <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo></math></span> cannot both have supports of finite measure. The second one is the Logvinenko–Sereda theorem, which provides a quantitative version of the uncertainty principle by showing that a function whose multidimensional Fourier–Bessel transform has bounded support can be controlled by its restriction to any relatively dense subset. Both results extend the corresponding one-dimensional uncertainty principles for the Fourier–Bessel transform to the multidimensional setting.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130414"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978925","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130431
Cyrille Kenne
Fokker-Planck equations are widely used to describe the evolution of probability density functions in stochastic systems, with applications ranging from physics and biology to finance and engineering. While these equations admit analytical solutions in certain linear or low-dimensional settings, their analysis becomes significantly more challenging for nonlinear systems, especially when combined with reflecting boundary conditions and external control inputs. Such settings are highly relevant in physical contexts, including confined diffusions and controlled transport phenomena. In this work, we study the optimal control of nonlinear Fokker-Planck equations subject to reflecting boundaries and pointwise control constraints. We rigorously establish the existence, uniqueness, and boundedness of solutions. Additionally, we prove regularity properties of the control-to-state mapping and derive first-order necessary optimality conditions in the form of variational inequalities coupled with an adjoint system. Our analysis employs the Schauder fixed-point theorem, De Giorgi's iteration, and functional analysis arguments, adapted to address the nonlinear structure of the problem. These results contribute to the theoretical understanding of controlled stochastic processes in nonlinear physical systems.
{"title":"Optimal control of nonlinear Fokker-Planck equations with reflecting boundary conditions","authors":"Cyrille Kenne","doi":"10.1016/j.jmaa.2026.130431","DOIUrl":"10.1016/j.jmaa.2026.130431","url":null,"abstract":"<div><div>Fokker-Planck equations are widely used to describe the evolution of probability density functions in stochastic systems, with applications ranging from physics and biology to finance and engineering. While these equations admit analytical solutions in certain linear or low-dimensional settings, their analysis becomes significantly more challenging for nonlinear systems, especially when combined with reflecting boundary conditions and external control inputs. Such settings are highly relevant in physical contexts, including confined diffusions and controlled transport phenomena. In this work, we study the optimal control of nonlinear Fokker-Planck equations subject to reflecting boundaries and pointwise control constraints. We rigorously establish the existence, uniqueness, and boundedness of solutions. Additionally, we prove regularity properties of the control-to-state mapping and derive first-order necessary optimality conditions in the form of variational inequalities coupled with an adjoint system. Our analysis employs the Schauder fixed-point theorem, De Giorgi's iteration, and functional analysis arguments, adapted to address the nonlinear structure of the problem. These results contribute to the theoretical understanding of controlled stochastic processes in nonlinear physical systems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130431"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023453","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130419
Haiyan Li , Marcelo M. Cavalcanti , Valeria N. Domingos Cavalcanti , Baowei Feng
In this article, a nonlinearly damped viscoelastic wave equation with supercritical source term and localized history memory is considered. We establish an exponential and a logarithmic energy decay rates of solutions, which are dependent on the behavior of the damping term. By using the property of a closed set of stable set for potential well, we derive the estimate which does not generate lower-order term. The standard lengthy compactness-uniqueness argument is completely avoided. Hence our proof is more concise and shorter. We also remove some strong conditions on initial data in previous result to obtain a weaker energy decay. In particular, we give a logarithmic decay rate under the weak additional assumption on initial data.
{"title":"Energy decay for a viscoelastic wave equation with supercritical source and localized history memory","authors":"Haiyan Li , Marcelo M. Cavalcanti , Valeria N. Domingos Cavalcanti , Baowei Feng","doi":"10.1016/j.jmaa.2026.130419","DOIUrl":"10.1016/j.jmaa.2026.130419","url":null,"abstract":"<div><div>In this article, a nonlinearly damped viscoelastic wave equation with supercritical source term and localized history memory is considered. We establish an exponential and a logarithmic energy decay rates of solutions, which are dependent on the behavior of the damping term. By using the property of a closed set of stable set for potential well, we derive the estimate which does not generate lower-order term. The standard lengthy compactness-uniqueness argument is completely avoided. Hence our proof is more concise and shorter. We also remove some strong conditions on initial data in previous result to obtain a weaker energy decay. In particular, we give a logarithmic decay rate under the weak additional assumption on initial data.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130419"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981215","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130420
Yafei Wen, Yuxiang Zhang
We propose a system of integrodifference equations to describe the interaction between pioneer and climax plant species with a seed bank. The invasion of the climax species is investigated by studying the existence of invasion spreading speeds and traveling waves. The recursion operator of the system is noncompact and nonmonotone, which makes the study of the existence of traveling wave solutions nontrivial. Another challenge is the estimation of invasion spreading speeds, which cannot be computed directly by the linearization method for monotone dynamical systems. We figure out a range of parameters, in which the existence of spreading speeds and their coincidence with the minimum wave speeds of traveling waves are established. By constructing suitable upper solutions, we present appropriate conditions under which the invasion spreading speed is linearly selected. We analytically confirm that the spreading speed of the invading species is strictly decreasing with respect to the fraction of non-germinating seeds in the seed bank.
{"title":"Invasion speeds and traveling waves for a pioneer-climax plant population model with a seed bank","authors":"Yafei Wen, Yuxiang Zhang","doi":"10.1016/j.jmaa.2026.130420","DOIUrl":"10.1016/j.jmaa.2026.130420","url":null,"abstract":"<div><div>We propose a system of integrodifference equations to describe the interaction between pioneer and climax plant species with a seed bank. The invasion of the climax species is investigated by studying the existence of invasion spreading speeds and traveling waves. The recursion operator of the system is noncompact and nonmonotone, which makes the study of the existence of traveling wave solutions nontrivial. Another challenge is the estimation of invasion spreading speeds, which cannot be computed directly by the linearization method for monotone dynamical systems. We figure out a range of parameters, in which the existence of spreading speeds and their coincidence with the minimum wave speeds of traveling waves are established. By constructing suitable upper solutions, we present appropriate conditions under which the invasion spreading speed is linearly selected. We analytically confirm that the spreading speed of the invading species is strictly decreasing with respect to the fraction of non-germinating seeds in the seed bank.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130420"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981217","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130409
Lorena Bociu , Matthew Broussard , Sarah Strikwerda
In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. We consider a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of poroelasticity equations is coupled with a systemic, 0D, lumped model of the remainder of the circulation. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the rest of the circulatory system. New results on wellposedness analysis of this multiscale model are provided.
{"title":"Existence and uniqueness of weak solutions to multiscale interface couplings of PDEs and ODEs for tissue perfusion","authors":"Lorena Bociu , Matthew Broussard , Sarah Strikwerda","doi":"10.1016/j.jmaa.2026.130409","DOIUrl":"10.1016/j.jmaa.2026.130409","url":null,"abstract":"<div><div>In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. We consider a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of poroelasticity equations is coupled with a systemic, 0D, lumped model of the remainder of the circulation. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the rest of the circulatory system. New results on wellposedness analysis of this multiscale model are provided.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130409"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038207","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}
Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130416
Maarten V. de Hoop , Kundan Kumar
We present a mixed dimensional model for a fractured poro-elastic medium including contact mechanics. The fracture is a lower dimensional surface embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a Darcy type model that follows the cubic law for permeability. The bulk poro-elasticity is governed by fully dynamic Biot equations. The resulting model is a mixed dimensional type where the fracture flow on a surface is coupled to a bulk flow and geomechanics model. The particularity of the work here is in considering fully dynamic Biot equation, that is, including an inertia term, and the contact mechanics including friction for the fracture surface. We prove the well-posedness of the continuous model.
{"title":"Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium","authors":"Maarten V. de Hoop , Kundan Kumar","doi":"10.1016/j.jmaa.2026.130416","DOIUrl":"10.1016/j.jmaa.2026.130416","url":null,"abstract":"<div><div>We present a mixed dimensional model for a fractured poro-elastic medium including contact mechanics. The fracture is a lower dimensional surface embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a Darcy type model that follows the cubic law for permeability. The bulk poro-elasticity is governed by fully dynamic Biot equations. The resulting model is a mixed dimensional type where the fracture flow on a surface is coupled to a bulk flow and geomechanics model. The particularity of the work here is in considering fully dynamic Biot equation, that is, including an inertia term, and the contact mechanics including friction for the fracture surface. We prove the well-posedness of the continuous model.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130416"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122689","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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