Nonlinear Analysis-Real World Applications最新文献

{"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}

{"title":"Traveling wave fronts for a diffusive spruce budworm model with spatio-temporal delay","authors":"Xinyan Wu,&nbsp;Guangsheng Lai,&nbsp;Zhiting Xu","doi":"10.1016/j.nonrwa.2025.104405","DOIUrl":"10.1016/j.nonrwa.2025.104405","url":null,"abstract":"<div><div>We revise a diffusive spruce budworm model with spatio-temporal (or nonlocal) delay. By choosing six distinct kernels, we find the wave speed <span><math><mrow><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mn>2</mn><msqrt><mrow><mi>r</mi><mi>d</mi></mrow></msqrt></mrow></math></span> to determine the existence of traveling wave fronts for the model, that is, the model admits a traveling wave front connecting the trivial equilibrium <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> and the positive equilibrium <span><math><mrow><mi>u</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> when <span><math><mrow><mi>c</mi><mo>≥</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. The approach is to combine the techniques of upper and lower solutions with the general theorem developed by Wang et al. (2006). The obtained results help us to understand the spreading patterns and the spreading speed of spruce budworm population.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104405"},"PeriodicalIF":1.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936506","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":"Hadamard fractional derivatives for a system of coupled implicit fractional pantograph differential equations","authors":"P. Palani ,&nbsp;D. Prabu ,&nbsp;Seenith Sivasundaram","doi":"10.1016/j.nonrwa.2025.104402","DOIUrl":"10.1016/j.nonrwa.2025.104402","url":null,"abstract":"<div><div>The purpose of this paper is to investigate the Hadamard fractional derivatives in a set of connected implicit fractional pantograph differential equations (FPDEs). This is a new and complex approach to looking at how these systems change over time. The study uses Banach and Schaefer’s fixed-point theorems to construct unique existence and stability conclusions that give fresh insights into the theoretical framework of fractional calculus in FPDEs. Illustrative examples are provided to demonstrate the applications and validate the theoretical results, underscoring the study’s contribution to advancing analytical methods for FPDEs.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104402"},"PeriodicalIF":1.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936507","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 of an inelastic contact problem for the damped wave equation","authors":"Boris Muha ,&nbsp;Srđan Trifunović","doi":"10.1016/j.nonrwa.2025.104408","DOIUrl":"10.1016/j.nonrwa.2025.104408","url":null,"abstract":"<div><div>In this paper, we examine the dynamic behavior of a viscoelastic string oscillating above a rigid obstacle in a one-dimensional setting, accounting for inelastic contact between the string and the obstacle. We construct a global-in-time weak solution to this problem by using an approximation method that incorporates a penalizing repulsive force of the form <span><math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ɛ</mi></mrow></mfrac><msub><mrow><mi>χ</mi></mrow><mrow><mrow><mo>{</mo><mi>η</mi><mo>&lt;</mo><mn>0</mn><mo>}</mo></mrow></mrow></msub><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>η</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo></mrow></msup></mrow></math></span>. The weak solution exhibits well-controlled energy dissipation, which occurs exclusively during contact and is concentrated on a set of zero measure, specifically when the string moves downward. Furthermore, the velocity is shown to vanish after contact in a specific weak sense. This model serves as a simplified framework for studying contact problems in fluid–structure interaction contexts.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104408"},"PeriodicalIF":1.8,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936508","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":"Darboux problem for perturbed hyperbolic fractional order differential inclusions with finite delay","authors":"Mohamed Helal ,&nbsp;Seenith Sivasundaram","doi":"10.1016/j.nonrwa.2025.104387","DOIUrl":"10.1016/j.nonrwa.2025.104387","url":null,"abstract":"<div><div>In general, perturbed hyperbolic fractional-order differential inclusions with finite delay present significant mathematical challenges in terms of existence, uniqueness, and stability of solutions. The existence of solutions for perturbed hyperbolic fractional order differential inclusions with finite delay is examined in this paper using the fixed-point theorem of Dhage for the sum of a contraction multivalued map and a completely continuous map in conjunction with the mixed generalized Lipschitz and Caratheodory’s conditions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104387"},"PeriodicalIF":1.8,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936505","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":"Well-posedness of the time-periodic Jordan–Moore–Gibson–Thompson equation","authors":"Barbara Kaltenbacher","doi":"10.1016/j.nonrwa.2025.104407","DOIUrl":"10.1016/j.nonrwa.2025.104407","url":null,"abstract":"<div><div>Motivated by applications of nonlinear ultrasonics under continuous wave excitation, we study the Jordan–Moore–Gibson–Thompson (JMGT) equation – a third order in time quasilinear PDE – under time periodicity conditions. Here the coefficient of the third order time derivative is the so-called relaxation time and a thorough understanding of the limiting behavior for vanishing relaxation time is essential to link these JMGT equations to classical second order models in nonlinear acoustics,</div><div>As compared to the meanwhile well understood initial value problem for JMGT, the periodic setting poses substantial challenges due to a loss of temporal regularity, while the analysis still requires a pointwise (in space and time) control on the magnitude of solutions in order to maintain stability or equivalently, to avoid degeneracy of the second time derivative coefficient.</div><div>We provide a full well-posedness analysis both in the presence and absence of gradient nonlinearity, as relevant for modeling non-cumulative nonlinear effects, under practically relevant mixed boundary conditions. The source-to-state map is thus well-defined and in addition we show it to be Lipschitz continuously differentiable, a result that is useful for inverse problems applications such as acoustic nonlinearity tomography. The energy bounds derived for the well-posedness analysis of periodic JMGT equations also allow to fully justify the singular limit for vanishing relaxation time.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104407"},"PeriodicalIF":1.8,"publicationDate":"2025-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936504","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":"Global and exponential stabilization of a chemotactic alopecia areata model with signal-dependent diffusion and sensitivity","authors":"Jing Zhang ,&nbsp;Shengmao Fu","doi":"10.1016/j.nonrwa.2025.104404","DOIUrl":"10.1016/j.nonrwa.2025.104404","url":null,"abstract":"<div><div>This paper focuses on the large time behavior of a three-component chemotaxis model with signal-dependent diffusion and sensitivity for alopecia areata (AA) which is a noncontagious autoimmune disorder. The model describes the complex interactions among the CD<span><math><msup><mrow><mn>4</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells, CD<span><math><msup><mrow><mn>8</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells and interferon-gamma (IFN-<span><math><mi>γ</mi></math></span>). Firstly, we use a method of weighted energy estimates to establish the uniform-in-time boundedness of classical solutions for the system when nonlinear proliferation rate is small compared with density-dependent death rates. Then, the globally exponentially asymptotic stability of positive equilibrium is proved if nonlinear proliferation rate and density-dependent death rates are within a particular range, and signal-dependent sensitivities are small relative to signal-dependent diffusions. Finally, some numerical simulations are performed to reveal the spatio-temporal dynamics of system in two space dimensions. It is shown that sparse and homogeneous hairless patches occur in or around diseased hair follicles (HFs) and eventually induce a stable AA if signal-dependent chemotactic effect is weak.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104404"},"PeriodicalIF":1.8,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928010","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}