Nonlinear Analysis-Real World Applications最新文献

{"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}

{"title":"Sensitivity analysis of a Signorini-type history-dependent variational inequality","authors":"Livia Betz ,&nbsp;Andaluzia Matei ,&nbsp;Mircea Sofonea","doi":"10.1016/j.nonrwa.2025.104394","DOIUrl":"10.1016/j.nonrwa.2025.104394","url":null,"abstract":"<div><div>We consider a history-dependent variational inequality <span><math><mrow><mi>P</mi></mrow></math></span> which models the frictionless contact between a viscoelastic body and a rigid obstacle covered by a layer of soft material. The inequality is expressed in terms of the displacement field, is governed by the data <span><math><mi>f</mi></math></span> (related to the applied body forces and surface tractions) and, under appropriate assumptions, it has a unique solution, denoted by <span><math><mi>u</mi></math></span>. Our aim in this paper is to perform a sensitivity analysis of the inequality <span><math><mrow><mi>P</mi></mrow></math></span>, including the study of the regularity of the solution operator <span><math><mrow><mi>f</mi><mo>↦</mo><mi>u</mi></mrow></math></span>. To this end, we start by proving the equivalence of <span><math><mrow><mi>P</mi></mrow></math></span> with a fixed point problem, denoted by <span><math><mrow><mi>Q</mi></mrow></math></span> (Theorem 2). We then consider an associated optimal control problem, for which we present an existence result (Theorem 6). Then, we prove the directional differentiability of the solution operator and show that the directional derivative at <span><math><mi>f</mi></math></span> in direction <span><math><mrow><mi>δ</mi><mi>f</mi></mrow></math></span> is characterized by a history-dependent variational inequality with time-dependent constraints (Theorem 14). Finally, we prove two well-posedness results in the study of Problems <span><math><mrow><mi>P</mi></mrow></math></span> and <span><math><mrow><mi>Q</mi></mrow></math></span>, respectively (Theorem 17), and compare the two well-posedness concepts employed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104394"},"PeriodicalIF":1.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143905986","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 boundedness in a chemotaxis-growth system with weak singular sensitivity in any dimensional setting","authors":"Minh Le ,&nbsp;Halil Ibrahim Kurt","doi":"10.1016/j.nonrwa.2025.104392","DOIUrl":"10.1016/j.nonrwa.2025.104392","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper concerns with the following parabolic–elliptic chemotaxis-growth system with weak singular sensitivity &lt;span&gt;&lt;span&gt;&lt;span&gt;(1)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;under no-flux boundary conditions in a smoothly bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; the parameters &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; are positive constants and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;In the past few years, there has been considerable interest in exploring whether logistic kinetics can sufficiently guarantee the global existence and boundedness of classical solutions or prevent finite-time blow-up in various chemotaxis models. In particular, significant results have been reported by numerous authors regarding system Eq. &lt;span&gt;&lt;span&gt;(1)&lt;/span&gt;&lt;/span&gt;. For instance, a recent study (Kurt 2025) demonstrated that Eq. &lt;span&gt;&lt;span&gt;(1)&lt;/span&gt;&lt;/span&gt; admits a globally bounded classical solution provided that &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is sufficiently large and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;It is then natural to ask whether the boundedness of classical solutions of Eq. &lt;span&gt;&lt;span&gt;(1)&lt;/span&gt;&lt;/span&gt; can be established independently of the condition connecting &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; or considering a milder condition for &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. This paper addresses this question by providing an extension of the upper bound for &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/spa","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104392"},"PeriodicalIF":1.8,"publicationDate":"2025-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904383","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":"Application of Stieltjes parabolic partial differential equations to the population dynamics of Vespa Velutina","authors":"Iván Area ,&nbsp;Francisco J. Fernández ,&nbsp;Juan J. Nieto ,&nbsp;F. Adrián F. Tojo","doi":"10.1016/j.nonrwa.2025.104388","DOIUrl":"10.1016/j.nonrwa.2025.104388","url":null,"abstract":"<div><div>In this work, we present a mathematical model based on Stieltjes differential equations to analyze the spread of <em>Vespa Velutina</em>. To this end, we start by defining a zero-dimensional model, which we later generalize to a two-dimensional model with a diagonalizable spatial differential operator. The advantage of considering Stieltjes differential equations lies in the fact that they allow us to naturally handle reproductive impulses due to the hatching of individuals and periods of inactivity resulting from hibernation. Finally, we present some numerical results obtained using real nest position data.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104388"},"PeriodicalIF":1.8,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143890753","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}