Nonlinear Analysis-Real World Applications最新文献

{"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":"<div><div>This paper concerns with the following parabolic–elliptic chemotaxis-growth system with weak singular sensitivity <span><span><span>(1)</span><span><math><mrow><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>u</mi></mrow><mrow><msup><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></mfrac><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>α</mi><mi>v</mi><mo>+</mo><mi>β</mi><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced><mspace></mspace></mrow></math></span></span></span>under no-flux boundary conditions in a smoothly bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn><mo>,</mo></mrow></math></span> the parameters <span><math><mrow><mi>χ</mi><mo>,</mo><mspace></mspace><mi>r</mi><mo>,</mo><mspace></mspace><mi>μ</mi><mo>,</mo><mspace></mspace><mi>α</mi><mo>,</mo><mspace></mspace><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are positive constants and <span><math><mrow><mi>k</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>.</mo></mrow></math></span></div><div>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. <span><span>(1)</span></span>. For instance, a recent study (Kurt 2025) demonstrated that Eq. <span><span>(1)</span></span> admits a globally bounded classical solution provided that <span><math><mi>μ</mi></math></span> is sufficiently large and <span><math><mrow><mi>k</mi><mo>&lt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn><mo>.</mo></mrow></math></span></div><div>It is then natural to ask whether the boundedness of classical solutions of Eq. <span><span>(1)</span></span> can be established independently of the condition connecting <span><math><mi>k</mi></math></span> and <span><math><mi>n</mi></math></span> or considering a milder condition for <span><math><mi>μ</mi></math></span>. This paper addresses this question by providing an extension of the upper bound for <span><math><mi>k</mi></math></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}

{"title":"A class of moving boundary problems with an exponential source term","authors":"Julieta Bollati ,&nbsp;Ernesto A. Borrego Rodriguez ,&nbsp;Adriana C. Briozzo ,&nbsp;Colin Rogers","doi":"10.1016/j.nonrwa.2025.104390","DOIUrl":"10.1016/j.nonrwa.2025.104390","url":null,"abstract":"<div><div>This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed face, through the application of a reciprocal transformation alongside the Cole–Hopf transformation. For specific cases, we derive explicit similarity solutions in parametric form. This innovative approach enhances our understanding of the underlying dynamics and offers valuable insights into the behavior of these systems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104390"},"PeriodicalIF":1.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143887695","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 semigroup of conservative weak solutions of the two-component Novikov equation","authors":"K.H. Karlsen ,&nbsp;Ya. Rybalko","doi":"10.1016/j.nonrwa.2025.104393","DOIUrl":"10.1016/j.nonrwa.2025.104393","url":null,"abstract":"<div><div>We study the Cauchy problem for the two-component Novikov system with initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> such that the product <span><math><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> belongs to <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>. We construct a global semigroup of conservative weak solutions. We also discuss the potential concentration phenomena of <span><math><mrow><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mi>u</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></math></span>, <span><math><mrow><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mi>v</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></math></span>, and <span><math><mrow><mfenced><mrow><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mi>u</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mi>v</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced><mi>d</mi><mi>x</mi></mrow></math></span>, which contribute to wave-breaking and may occur for a set of time with nonzero measure. Finally, we establish the continuity of the data-to-solution map in the uniform norm.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104393"},"PeriodicalIF":1.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881935","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":"The energy equality of the Navier–Stokes equations in the framework of Besov-Lorentz type spaces, and its application to the MHD system","authors":"Taichi Eguchi","doi":"10.1016/j.nonrwa.2025.104389","DOIUrl":"10.1016/j.nonrwa.2025.104389","url":null,"abstract":"<div><div>We find a new refined sufficient condition to establish the energy equality of the incompressible Navier–Stokes equations in the framework of the Besov–Lorentz type space. By virtue of the larger Besov–Lorentz type space than the usual Besov space, our result may include the previous result of Cheskidov–Luo (2020). As an application of our results on the Navier–Stokes equations, we obtain a new sufficient condition to establish the energy equality of the MHD system. Our result may also cover author’s previous result (2024) on the validity of the energy equality of the MHD system. Moreover, it should be noted that our sufficient condition of the magnetic field is strictly weaker than that of the Navier–Stokes equations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104389"},"PeriodicalIF":1.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881934","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 well-posedness and large time behaviors for the generalized MHD equations","authors":"Huan Yu ,&nbsp;Haifeng Shang","doi":"10.1016/j.nonrwa.2025.104384","DOIUrl":"10.1016/j.nonrwa.2025.104384","url":null,"abstract":"<div><div>In this paper, we are concerned with the <span><math><mi>n</mi></math></span>D generalized MHD equations. By using a new approach, different from the classical Fourier splitting method developed by Schonbek (Schonbek, 1985, 1986) and the spectral representation technique (Kajikiya and Miyakawa, 1986), we recover and improve some known decay results of weak solutions. Besides, by rewriting the nonlinear terms into new commutators to efficiently distribute derivatives, we obtain the existence, uniqueness and optimal decay estimates of global solutions for the <span><math><mi>n</mi></math></span>D generalized MHD equations with small dissipation index <span><math><mi>β</mi></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104384"},"PeriodicalIF":1.8,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878962","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":"Exploring predator–prey dynamics: Integrating competitor predators, harvesting delay and fear effect on prey with a modified Beddington–DeAngelis functional response","authors":"Anuj Kumar Umrao,&nbsp;Prashant K. Srivastava","doi":"10.1016/j.nonrwa.2025.104391","DOIUrl":"10.1016/j.nonrwa.2025.104391","url":null,"abstract":"<div><div>Selective harvesting is a vital strategy for controlling over-exploitation and protecting the incidental killing of juvenile species. To ensure that the individuals reach a suitable age or size before being harvested, a specific time delay, known as harvesting-induced delay, should be maintained. Also, predators can indirectly slow down the growth rate of prey by inducing fear in them, which affects their behaviour and reproduction. In this work, we study a predator–prey model to examine the impact of predator selective (delayed) harvesting in the presence of fear in prey species and the interspecific competition of predator with the competitive predator. It is assumed that the density of the competitive predator is constant and both predators induce fear in prey. We determine the conditions related to the existence of transcritical and Hopf bifurcations for the non-delay case, and various delay-induced scenarios via Hopf bifurcation. We also numerically explore the impact of delayed harvesting on the system dynamics by simultaneously varying the harvesting effort, fear level, and the interspecific competition with competitive predator in bi-parametric planes. It is observed that the harvesting delay can result in stability invariance, instability invariance, stability change, instability switching, and stability switching phenomena under varied parametric conditions. Further, when the harvesting delay is fixed, the equilibrium point experiences instability invariance and instability change, instability change and instability switching, and instability invariance, stability change and stability switching with respect to the harvesting effort, the interspecific competition, and the fear level, respectively. Our findings indicate that regulated selective harvesting of predator, and a moderate level of fear in prey and interspecific competition with the competitive predator are essential for maintaining stability and coexistence in the ecosystem. The rich and complex dynamics holds significance from a biological viewpoint and may potentially impact the population management strategies.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104391"},"PeriodicalIF":1.8,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881933","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":"A class of time-dependent quasi-variational–hemivariational inequalities with applications","authors":"Yongjian Liu ,&nbsp;Stanisław Migórski ,&nbsp;Sylwia Dudek","doi":"10.1016/j.nonrwa.2025.104385","DOIUrl":"10.1016/j.nonrwa.2025.104385","url":null,"abstract":"<div><div>In this paper a class of time-dependent multivalued quasi-variational inequalities of elliptic type with a solution dependent constraint set, is studied. Its solvability and the closedness of the solution set are proved. Then, the results are applied to constrained quasi-variational–hemivariational inequalities for which the relaxed monotonicity condition is not required. Finally, the abstract results are illustrated by two applications. The first one is a time-dependent frictional contact problem with locking materials, and the second one is the stationary incompressible Navier–Stokes equation which models a generalized Newtonian fluid of Bingham type. Results on existence and the closedness of the solution sets are established for both applications.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104385"},"PeriodicalIF":1.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874274","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":"Addendum to “Γ-convergence involving nonlocal gradients with varying horizon: Recovery of local and fractional models” [Nonlinear Analysis: Real World Applications, Volume 85 (2025), 104371]","authors":"Javier Cueto ,&nbsp;Carolin Kreisbeck ,&nbsp;Hidde Schönberger","doi":"10.1016/j.nonrwa.2025.104386","DOIUrl":"10.1016/j.nonrwa.2025.104386","url":null,"abstract":"","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104386"},"PeriodicalIF":1.8,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168575","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}