Nonlinear Analysis-Real World Applications最新文献

{"title":"On a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage","authors":"Giulia Cavalleri ,&nbsp;Pierluigi Colli ,&nbsp;Alain Miranville ,&nbsp;Elisabetta Rocca","doi":"10.1016/j.nonrwa.2025.104419","DOIUrl":"10.1016/j.nonrwa.2025.104419","url":null,"abstract":"<div><div>In this paper, we study a nonlinearly coupled initial–boundary value problem describing the evolution of brain tumor growth, including lactate metabolism. In our modeling approach, we also take into account the viscoelastic properties of the tissues as well as the reversible damage effects that could occur, possibly caused by surgery. After introducing the PDE system, coupling a Fischer–Kolmogorov type equation for the tumor phase with a reaction–diffusion equation for the lactate, a quasi-static momentum balance with nonlinear elasticity and viscosity matrices, and a nonlinear differential inclusion for the damage, we prove the existence of global in time weak solutions under reasonable assumptions on the involved functions and data. Strengthening these assumptions, we subsequently prove further regularity properties of the solutions as well as their continuous dependence with respect to the data, entailing the well-posedness of the Cauchy problem associated with the nonlinear PDE system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104419"},"PeriodicalIF":1.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178557","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}

{"title":"Mathematical analysis and numerical simulation of a nonlinear radiofrequency ablation model in cardiac tissue","authors":"Mostafa Bendahmane ,&nbsp;Youssef Ouakrim ,&nbsp;Yassine Ouzrour ,&nbsp;Mohamed Zagour","doi":"10.1016/j.nonrwa.2025.104412","DOIUrl":"10.1016/j.nonrwa.2025.104412","url":null,"abstract":"<div><div>This paper deals with the mathematical analysis and numerical simulation of a new nonlinear ablation system modeling radiofrequency ablation phenomena in cardiac tissue, which incorporates the effects of blood flow on the heat generated when ablation by radiofrequency. The model also considers the effects of viscous energy dissipation. It consists of a coupled thermistor problem and the incompressible Navier–Stokes equations that describe the evolution of temperature, velocity and potential in cardiac tissue. In addition to Faedo–Galerkin method, we use Schauder’s fixed-point theory to prove the existence of the weak solutions in two- and three-dimensional space. Moreover, we prove the uniqueness of the solution under some additional conditions on the data and the solution. Finally, we discuss some numerical results for the validation of the proposed model using the finite element method.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104412"},"PeriodicalIF":1.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166243","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}

{"title":"Existence and global behaviour of solutions of a parabolic problem involving the fractional p-Laplacian in porous medium","authors":"Loïc Constantin,&nbsp;Jacques Giacomoni,&nbsp;Guillaume Warnault","doi":"10.1016/j.nonrwa.2025.104416","DOIUrl":"10.1016/j.nonrwa.2025.104416","url":null,"abstract":"<div><div>In this paper, we prove the existence and the uniqueness of a weak and mild solution of the following nonlinear parabolic problem involving the porous <span><math><mi>p</mi></math></span>-fractional Laplacian: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>×</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>∖</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>⋅</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>We also study further the the homogeneous case <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi></mrow></math></span> with <span><math><mrow><mi>q</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. In particular we investigate global time existence, uniqueness, global behaviour of weak solutions and stabilization.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104416"},"PeriodicalIF":1.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166342","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}

{"title":"Stability of steady-state solutions of a class of Keller–Segel type models with linear sensitivity and nonlinear consumption rate of chemical stimuli","authors":"Zefu Feng,&nbsp;Luyao Wang","doi":"10.1016/j.nonrwa.2025.104417","DOIUrl":"10.1016/j.nonrwa.2025.104417","url":null,"abstract":"<div><div>This paper is devoted to the study of a class of Keller–Segel type models with Dirichlet boundary conditions and zero-flux boundary conditions on a one-dimensional bounded interval. We show the existence of non-trivial steady state solutions of these models by using sub-super solutions method and standard monotone iteration scheme method. Furthermore, we also show that the steady-state solution of these models is nonlinearly asymptotically stable by using the inverse derivative technique if the initial perturbation is sufficiently small.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104417"},"PeriodicalIF":1.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166343","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}

{"title":"Existence of a weak solution to the Yamabe type flow","authors":"Sitao Zhang","doi":"10.1016/j.nonrwa.2025.104418","DOIUrl":"10.1016/j.nonrwa.2025.104418","url":null,"abstract":"<div><div>In this paper, we study a doubly nonlinear parabolic equation, which is the Yamabe type heat flow on a bounded regular domain in Euclidean space. We show that under suitable assumptions on the initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. We show the existence of a weak solution to the Yamabe type heat flow.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104418"},"PeriodicalIF":1.8,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144154677","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}

{"title":"Blow-up of a nonlinear reaction–diffusion system with nonlocal weighted exponential boundary condition","authors":"Hongwei Liu ,&nbsp;Lingling Zhang ,&nbsp;Tao Liu","doi":"10.1016/j.nonrwa.2025.104413","DOIUrl":"10.1016/j.nonrwa.2025.104413","url":null,"abstract":"<div><div>In this paper, we study a class of reaction–diffusion system with nonlinear terms, variable coefficients, and nonlocal exponential boundary conditions. We demonstrate the existence of solutions using the subsolution and supersolution method, comparison principle, and representation theorem. Uniqueness of solutions is established via the contraction mapping principle, aided by the Green’s function. Furthermore, we construct supersolutions to prove the existence of global solutions under various conditions. By employing the auxiliary function method, we obtain upper and lower bounds for blow-up solutions under different parametric settings. Finally, examples are provided to verify our theoretical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104413"},"PeriodicalIF":1.8,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124271","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}

{"title":"Solutions of non-homogeneous linear set-valued differential equations","authors":"Uma Maheswara Rao Epuganti,&nbsp;Gnana Bhaskar Tenali","doi":"10.1016/j.nonrwa.2025.104411","DOIUrl":"10.1016/j.nonrwa.2025.104411","url":null,"abstract":"<div><div>We study the linear non-homogeneous set-valued differential equations involving a notion of generalized derivative that includes the Hukuhara, Bede–Gal (BG), and Plotnikov–Skripnik (PS) derivatives. We consider the associated initial value problems and, using their equivalent integral equations, obtain some general as well as constructive formulas for the solutions. Several illustrative examples are provided.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104411"},"PeriodicalIF":1.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124270","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}

{"title":"Travelling waves in a dispersion–saturating diffusion equation","authors":"Gnord Maypaokha ,&nbsp;Nabil Bedjaoui ,&nbsp;Joaquim M.C. Correia ,&nbsp;Michael Grinfeld","doi":"10.1016/j.nonrwa.2025.104403","DOIUrl":"10.1016/j.nonrwa.2025.104403","url":null,"abstract":"<div><div>In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau–Korteweg de Vries equation. We establish existence as well as linear and nonlinear determinacy results in different regimes.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104403"},"PeriodicalIF":1.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106502","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}

{"title":"Integral representations of lower semicontinuous envelopes and Lavrentiev phenomenon for non continuous Lagrangians","authors":"Tommaso Bertin","doi":"10.1016/j.nonrwa.2025.104414","DOIUrl":"10.1016/j.nonrwa.2025.104414","url":null,"abstract":"<div><div>We consider the functional <span><span><span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>∞</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mo>∇</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mi>d</mi><mi>x</mi><mspace></mspace><mi>u</mi><mo>∈</mo><mi>φ</mi><mo>+</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mi>∞</mi></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span></span></span>where <span><math><mi>Ω</mi></math></span> is an open bounded Lipschitz subset of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> and <span><math><mrow><mi>φ</mi><mo>∈</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>. We do not assume neither convexity or continuity of the Lagrangian w.r.t. the last variable. We prove that, under suitable assumptions, the lower semicontinuous envelope of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> both in <span><math><mrow><mi>φ</mi><mo>+</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> and in the larger space <span><math><mrow><mi>φ</mi><mo>+</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> can be represented by means of the bipolar <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>∗</mo><mo>∗</mo></mrow></msup></math></span> of <span><math><mi>f</mi></math></span>. In particular we can also exclude Lavrentiev Phenomenon between <span><math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> for autonomous Lagrangians.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104414"},"PeriodicalIF":1.8,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106501","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}

{"title":"Analysis and optimization of tumor inhibitor treatments in a free boundary tumor growth model","authors":"Xinyue Evelyn Zhao","doi":"10.1016/j.nonrwa.2025.104406","DOIUrl":"10.1016/j.nonrwa.2025.104406","url":null,"abstract":"<div><div>This paper investigates a free boundary model describing the growth of a spherical tumor in the presence of inhibitors. Specifically, we analyze the optimal inhibitor concentration to minimize both tumor size and side effects of the inhibitor. We establish the existence and uniqueness of the optimal control, and provide a characterization of the optimal control. Numerical simulations illustrate how the optimal control strategy varies with different emphases on controlling tumor size throughout the treatment period and at its terminal time. The findings indicate that when the focus is on controlling tumor size throughout the treatment, a higher dose is administered initially; conversely, when the objective is to minimize tumor size at the treatment’s end, a higher dose is applied towards the end of the treatment period. Additionally, we explore the impact of varying parameters on the optimal control strategy. The optimal treatment dosages might be adjusted based on factors such as maximum tolerated concentrations, the severity of side effects, and the rates at which side effects decay.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104406"},"PeriodicalIF":1.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090391","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}