Nonlinear Analysis-Real World Applications最新文献

{"title":"Boundedness and large-time behavior in a two-species doubly degenerate diffusion chemotaxis system with logistic proliferation","authors":"Yuting Xiang","doi":"10.1016/j.nonrwa.2025.104525","DOIUrl":"10.1016/j.nonrwa.2025.104525","url":null,"abstract":"<div><div>The two-species doubly degenerate nutrient taxis model with competitive kinetics<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><mrow></mrow><msub><mi>u</mi><mrow><mn>1</mn><mi>t</mi></mrow></msub></mrow></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>1</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>1</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>1</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>u</mi><mrow><mn>2</mn><mi>t</mi></mrow></msub></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>2</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>2</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>2</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>2</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>2</mn></msub><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>v</mi><mi>t</mi></msub></mtd><mtd><mrow><mo>=</mo><msub><mi>v</mi><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>−</mo><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mi>v</mi><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>is considered under no-flux boundary conditions in an open bounded interval <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi></mrow></math></span>, where <span><math><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mi>μ</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> for <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>. It is shown that for all suitably regular nonnegative initial data <span><math><mrow><mo>(</mo><msub><mi>u</mi><mn>10</mn></msub><mo>,</mo><msub><mi>u</mi><mn>20</mn></msub><mo>,</mo><msub><mi>v</mi><mn>0</mn></msub><mo>)</mo></mrow></math></span>, where <span><math><ms","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104525"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418267","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 note on the logistic damping effect to ensure the global solvability of the chemotaxis system with degenerate signal-dependent motility","authors":"Quanyong Zhao, Jinrong Wang","doi":"10.1016/j.nonrwa.2025.104520","DOIUrl":"10.1016/j.nonrwa.2025.104520","url":null,"abstract":"<div><div>This paper is devoted to investigating the logistic source damping effect of the following model<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>u</mi><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mi>u</mi><mi>α</mi></msup><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>v</mi><mi>t</mi></msub><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><mi>u</mi><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>under homogeneous Neumann boundary conditions in a smooth bounded domain <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mi>n</mi></msup></mrow></math></span>, where <span><math><mrow><mi>r</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mi>μ</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>></mo><mn>1</mn></mrow></math></span> are constants. For the case <span><math><mrow><mrow><mo>(</mo><mi>φ</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mo>[</mo><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>]</mo></mrow><mn>2</mn></msup><mo>,</mo><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>></mo><mn>0</mn><mspace></mspace><mtext>and</mtext><mspace></mspace><mfrac><msup><mrow><mo>|</mo><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>|</mo></mrow><mn>2</mn></msup><mrow><mi>φ</mi><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mfrac></mrow></math></span> is bounded on <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span>, generating the prototypical choice given by <span><math><mrow><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>v</mi><mrow><mo>−</mo><mi>k</mi></mrow></msup></mrow></math></span> and <span><math><mrow><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>k</mi><msup><mi>v</mi><mrow><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> with <span><math><mrow><mi>k</mi><mo>></mo><mn>0</mn></mrow></math></span>, it is shown that even with large initial data, the existence of the global classical solution to the above problem can be achieved when <span><math><mrow><mi>α</mi><mo>></mo><mn>3</mn><mo>−</mo><mfrac><mn>6</mn><mrow><mi>n</mi><mo>+</mo><mn>4</mn></mrow></mfrac></mrow></math></span> with <span><math><mrow","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104520"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364267","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 existence and optimal time-decay rates of 3D non-isentropic compressible Navier-Stokes system with potential force","authors":"Wenwen Huo ,&nbsp;Chao Zhang","doi":"10.1016/j.nonrwa.2025.104535","DOIUrl":"10.1016/j.nonrwa.2025.104535","url":null,"abstract":"<div><div>This paper concerns the global existence and optimal time-decay rate for the higher-order spatial derivative of classical solutions for the three-dimensional viscous and heat-conductive fluids, which is governed by the compressible Navier-Stokes (CNS) system with an external potential force. We first establish the global existence of the non-isentropic CNS system with potential force when the initial data is a small perturbation near the equilibrium state. Subsequently, we show the upper and lower bounds of the optimal decay rates for the solution and its spatial derivatives based on energy estimate and low-high frequency decomposition.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104535"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474364","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 strong solutions for 3-D immiscible and slightly compressible two-phase flow in porous media","authors":"Lei Xu ,&nbsp;Mengxue Du","doi":"10.1016/j.nonrwa.2025.104531","DOIUrl":"10.1016/j.nonrwa.2025.104531","url":null,"abstract":"<div><div>In this paper, we consider the flow of two-phase slightly compressible and immiscible fluids in porous media. We focus on the case where the densities of phases follow exponential laws with small compressibility factors, the absolute permeability is linked to the porosity via a Kozeny-Carman relation, and source terms account for realistic injection and production rates. Under some realistic hypotheses based on the data, we establish the local existence and uniqueness of strong solutions for the regularized three-dimensional system. We further show that the solution is global under small assumptions for the system without source terms. This is the first high-dimensional result of the strong solution without any symmetric assumptions for immiscible two-phase flow systems in porous media.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104531"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528543","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 existence and optimal time-decay rates of the compressible Navier-Stokes-Poisson equations with Cattaneo heat conduction","authors":"Fei Wu ,&nbsp;Yakui Wu","doi":"10.1016/j.nonrwa.2025.104545","DOIUrl":"10.1016/j.nonrwa.2025.104545","url":null,"abstract":"<div><div>Cattaneo heat conduction law is a hyperbolic type equation describing the finite speed of heat conduction. Compared to the classical Fourier heat conduction law, Cattaneo’s law provides a more accurate description of heat conduction in materials with high thermal conductivity and short time scales. In this paper, we study the global well-posedness and large-time behavior of the compressible Navier-Stokes-Poisson equations with Cattaneo heat conduction, which is from the dynamic of charged particles. We obtain the optimal time-decay rates of the high-order spatial derivatives of the solution. The decay rates of the solution reveal two conclusions: 1. due to the damping structure of Cattaneo’s law, the heat flux decays to the motionless state at a faster time-decay rate compared with velocity and temperature; 2. the decay rate of heat flux is same as that of density, and the latter has a faster decay rate because of the dispersion effect of the electric field. Finally, we also establish the convergence from the compressible Navier-Stokes-Poisson equations with Cattaneo heat conduction to the classical compressible Navier-Stokes-Poisson equations with Fourier heat conduction.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104545"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579379","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 existence of weak solutions to a cell migration and (de)differentiation model with double haptotaxis in the context of tissue regeneration","authors":"Nishith Mohan,&nbsp;Christina Surulescu","doi":"10.1016/j.nonrwa.2025.104516","DOIUrl":"10.1016/j.nonrwa.2025.104516","url":null,"abstract":"<div><div>We study a model for the spread and (de)differentiation of mesenchymal stem cells and chondrocytes in a scaffold whose fibers are coated with hyaluron. The chondrocytes produce new extracellular matrix, which, together with hyaluron, serves as a haptotactic cue for the stem cell migration. We prove global existence of weak solutions of the corresponding cross-diffusion system with double haptotaxis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104516"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333576","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":"Spatial profiles of a diffusion-advection epidemic model with saturated incidence mechanism and birth-death effect","authors":"Xiaodan Chen,&nbsp;Renhao Cui","doi":"10.1016/j.nonrwa.2025.104524","DOIUrl":"10.1016/j.nonrwa.2025.104524","url":null,"abstract":"<div><div>In this paper, we are concerned with a diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with saturated incidence mechanism and birth-death effect. The basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> has been derived through a variational expression and determined the threshold dynamics. We mainly investigate spatial profiles of endemic equilibrium with respect to large advection, small dispersal of susceptible/infected individuals and large saturation. These results may offer some prospective applications on disease control and prediction.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104524"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424894","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":"Time-delayed generalized Korteweg–de Vries-Burgers equation: Well-posedness and exponential decay","authors":"Ibtissam Issa,&nbsp;Cristina Pignotti","doi":"10.1016/j.nonrwa.2025.104519","DOIUrl":"10.1016/j.nonrwa.2025.104519","url":null,"abstract":"<div><div>This study explores the generalized Korteweg-de Vries-Burgers equation incorporating delay feedback and a damping term. Using semigroup arguments and Lyapunov functional techniques, we establish the existence of a global solution when the exponent of the nonlinear term satisfies some growth conditions. Furthermore, we prove exponential stability estimates under suitable assumptions: first in the case of a positive damping coefficient, then within a more comprehensive framework, accommodating sign changes in both coefficients, i.e. for the damping and the delay feedback. In both cases, we adopt refined conditions on the delay feedback’s coefficient, extending and enhancing existing results in the literature. In particular, our conditions are independent of the time delay size.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104519"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364266","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":"Spreading speeds for a Lotva-Volterra competition system with advection in a periodic habitat","authors":"Hong-Jie Wu,&nbsp;Bang-Sheng Han,&nbsp;Hong-Lei Wei,&nbsp;Yinghui Yang","doi":"10.1016/j.nonrwa.2025.104528","DOIUrl":"10.1016/j.nonrwa.2025.104528","url":null,"abstract":"<div><div>The study investigates pulsating wave speeds in an advective two-species competition-diffusion system under periodic environments. Recent studies have confirmed the existence and characterized the qualitative dynamics of pulsating waves. In this paper, we determine pulsating wave speed’s signs with identical diffusion rates and characterize invasion dynamics of competing species in heterogeneous environments by comparing the reactions and competitions. Specifically, we first establish a criterion for zero-speed waves and derive sufficient conditions for strictly positive or negative speeds. Our framework extends previous studies (e.g., Ding and Liang, Math. Ann. 385 (2023), 1–36) by considering functional representation of periodic steady-state solutions and explicit inclusion of advection effects and extends (e.g., Du et al., Z. Angew. Math. Phys. 71 (2020), 27 pp.) by further considering the sign of the pulsating wave speed, determining the long-time behavior of two strongly competing species. Crucially, the presence of the advection term indeed exerts a certain influence on the long-time behavior of two strongly competing species: From the perspective of the proof process, the appearance of the advection term increased the difficulty and complexity of proving Lemmas 2.3 and 3.1; from the result perspective, the advection term necessitates specific structural conditions for definitive speed determination. These findings advance understanding of pattern selection mechanisms in flow-driven ecological systems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104528"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474332","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":"Singularities of solutions to the non-Newtonian polytropic filtration","authors":"Meiling Zhou,&nbsp;Liangwei Wang,&nbsp;Jingxue Yin,&nbsp;Can Lu","doi":"10.1016/j.nonrwa.2025.104518","DOIUrl":"10.1016/j.nonrwa.2025.104518","url":null,"abstract":"<div><div>In this paper, we study the non-Newtonian polytropic filtration equation <span><math><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>−</mo><mi>div</mi><mrow><mo>(</mo><msup><mrow><mo>|</mo><mrow><mi>∇</mi><msup><mi>u</mi><mi>m</mi></msup></mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>∇</mi><msup><mi>u</mi><mi>m</mi></msup><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> with a positive initial data on a smooth bounded domain <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mi>n</mi></msup></mrow></math></span> for <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, where <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>m</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mi>m</mi></mfrac></mrow></math></span>, and in particular <span><math><mrow><mi>p</mi><mo>&lt;</mo><mfrac><mrow><mi>n</mi><mrow><mo>(</mo><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>+</mo><mi>m</mi><mi>n</mi></mrow></mfrac></mrow></math></span>. To investigate the regularity of solutions to the Dirichlet problem for this equation when the initial data exhibit a singularity of the form <span><math><mrow><msub><mi>u</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∼</mo><mi>A</mi><msup><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mrow><mo>−</mo><mi>γ</mi></mrow></msup></mrow></math></span> for <span><math><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math></span> with <span><math><mrow><mi>A</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>γ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, we introduce a linear diffusion term in the regularization process. This addition ensures that the equation remains uniformly parabolic, thereby satisfying both the maximum principle and the comparison principle. The desired results are obtained provided that the coefficient of this regularization term converges to zero in the norm of the appropriate function space. This paper shows that the behavior of the solution depends critically on the value of the exponent <span><math><mi>γ</mi></math></span> in the initial data, leading to the following distinct cases: finite-time boundedness, infinite-time boundedness, singular stabilization, and infinite-time blow-up.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104518"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333575","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}