Nonlinear Analysis-Real World Applications最新文献

{"title":"On the boundary stabilization of the KdV–KdV system with time-dependent delay","authors":"Roberto de A. Capistrano-Filho ,&nbsp;Boumediène Chentouf ,&nbsp;Victor H. Gonzalez Martinez ,&nbsp;Juan Ricardo Muñoz","doi":"10.1016/j.nonrwa.2024.104122","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104122","url":null,"abstract":"<div><p>The boundary stabilization problem of the Boussinesq KdV–KdV type system is investigated in this paper. An appropriate boundary feedback law consisting of a linear combination of a damping mechanism and a delay term is designed. Then, considering time-varying delay feedback together with a smallness restriction on the length of the spatial domain and the initial data, we show that the problem under consideration is well-posed. The proof combines Kato’s approach and the fixed-point argument. Last but not least, we prove that the energy of the linearized KdV–KdV system decays exponentially by employing the Lyapunov method.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140328571","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":"Self-similar solutions for the heat equation with a positive non-Lipschitz continuous, semilinear source term","authors":"A. Farina,&nbsp;R. Gianni","doi":"10.1016/j.nonrwa.2024.104121","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104121","url":null,"abstract":"<div><p>We investigate the existence of self-similar solutions for the parabolic equation <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msup><mi>H</mi><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow></math></span>, with <span><math><mrow><mn>0</mn><mo>≤</mo><mi>m</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span> and <span><math><mi>H</mi></math></span> the Heaviside graph, coupled with the initial datum <span><math><mrow><mi>u</mi><mfenced><mrow><mi>x</mi><mo>,</mo><mn>0</mn></mrow></mfenced><mo>=</mo><mo>−</mo><mi>c</mi><msup><mrow><mfenced><mrow><msup><mrow><mfenced><mrow><mi>x</mi></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mo>−</mo><mi>m</mi></mrow></mfrac></mrow></msup></mrow></math></span>, with <span><math><mrow><mi>c</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We analyze two cases: the problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> , <span><math><mrow><mi>n</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>, with <span><math><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow></math></span> and the problem in <span><math><mi>R</mi></math></span> when <span><math><mrow><mn>0</mn><mo>≤</mo><mi>m</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>. In the first case we extend the result of Gianni and Hulshof (1992) and show that there exist only two self-similar solutions changing sign, provided <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>c</mi><mo>&lt;</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>c</mi><mi>r</mi></mrow></msub></mrow></math></span>, with <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>c</mi><mi>r</mi></mrow></msub></math></span> obtained solving a specific algebraic equation depending on <span><math><mi>n</mi></math></span>. In the second case we prove that there exist at least two self-similar solutions of problem <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msup><mi>H</mi><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow></math></span>, <span><math><mrow><mi>u</mi><mfenced><mrow><mi>x</mi><mo>,</mo><mn>0</mn></mrow></mfenced><mo>=</mo><mo>−</mo><mi>c</mi><msup><mrow><mfenced><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mo>−</mo><mi>m</mi></mrow></mfrac></mrow></msup></mrow></math></span>, changing sign and evolving region where <span><math><mrow><mi>u</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. These solutions are of great interest. Indeed, on one hand they prove that the problem does not admit uniqueness and on the other they prove that a single point where <span><math><mrow><mi>u</mi><mfenced><mrow","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140296820","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":"Persistence or disappearance dynamics of a vector-borne disease model with climate change and distributed delay","authors":"Chufen Wu ,&nbsp;Jianshe Yu ,&nbsp;Dawei Zhang","doi":"10.1016/j.nonrwa.2024.104120","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104120","url":null,"abstract":"<div><p>This paper is concerned with the dual influences of climate change and distributed delay on dynamics of a vector-borne disease model. Compared to the previous works, the effect of climate change in a latent infection model is first considered since it increases the viral transmission probability of cross species. To deal with the non-monotonicity and heterogeneity of the model, we use some new ideas to investigate the spatio-temporal dynamics. The theoretical analyses suggest that three scenarios will occur as follows (i) If the disease persistence ahead of the climate change, the disease will die out by limiting the propagation speed of susceptible or infected individuals. (ii) The emergence of pulse type epidemic wave is obtained, which means the disease switches rapidly between persistence and disappearance. (iii) If susceptible individuals track the speed of climate change while infected individuals do not, the disease cannot evolve to the endemic disease.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140187146","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 torsion problem of the p-Bilaplacian","authors":"Andrei Grecu ,&nbsp;Mihai Mihăilescu","doi":"10.1016/j.nonrwa.2024.104117","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104117","url":null,"abstract":"<div><p>For each bounded and open set <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> (<span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>) with smooth boundary denoted by <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span> and each real number <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> we analyze the torsion problem of the <span><math><mi>p</mi></math></span>-Bilaplacian, namely <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mi>Δ</mi><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>Δ</mi><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span> in <span><math><mi>Ω</mi></math></span> with <span><math><mrow><mi>u</mi><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> on <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span>. Firstly, we show that for each <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> the problem has a unique weak solution <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. Secondly, we prove that <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> converges uniformly, as <span><math><mrow><mi>p</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, in <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow></mrow></math></span> to a certain function, say <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, which is exactly the unique solution of the problem <span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mn>1</mn></mrow></math></span> in <span><math><mi>Ω</mi></math></span> with <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> on <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span>. Moreover, for each real number <span><math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>Δ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></math></span> converges strongly to <span><math><mrow><mi>Δ</mi><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, as <span><math><mrow><mi>p</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. Next, we show that each solution <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is also a solution for the minimization problem <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>p</mi><mo>;</mo><mi>Ω</mi><mo>)</mo></mrow><mo>≔</mo>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140179675","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":"Enriched spatiotemporal dynamics of a model of Ebola transmission with a composite incidence function and density-independent treatment","authors":"Calvin Tadmon ,&nbsp;Jacques Ndé Kengne","doi":"10.1016/j.nonrwa.2024.104118","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104118","url":null,"abstract":"<div><p>In this work, we are concerned with the mathematical modeling and analysis of Ebola virus disease dynamics. Firstly, we design and analyze a nonlinear ordinary differential equations model integrating both direct and indirect transmission pathways with density-independent treatment and a composite nonlinear incidence function. We begin the analysis by proving the global existence of a unique positive and bounded solution. Then we compute the basic reproduction number on which relies the global dynamics of the model. We precisely show the existence of a unique disease-free equilibrium and that of a unique endemic equilibrium, and prove their global stability under appropriate assumptions on the basic reproduction number. Moreover, we perform the global sensitivity analysis of the basic reproduction number to assess the variability in the model predictions. We find that the forecasts closely agree with the 2014 outbreaks of the disease in Liberia and Sierra Leone. Secondly, we enrich this first model by extending it to a partially degenerate reaction–diffusion system via the inclusion of Fickian diffusion for susceptible and non-hospitalized infectious individuals in order to understand the dynamics of the disease transmission in a spatially homogeneous environment. We prove the global stability of the disease-free equilibrium and the uniform persistence when the basic reproduction number lies below and above one, respectively. Finally, numerical simulations are performed to illustrate some theoretical results obtained.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140179604","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 and stability of a predator–prey model with alarm-taxis","authors":"Songzhi Li ,&nbsp;Kaiqiang Wang","doi":"10.1016/j.nonrwa.2024.104119","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104119","url":null,"abstract":"<div><p>This paper deals with the global boundedness and stability of classical solutions to an important alarm-taxis ecosystem that is significant in understanding the behaviors of prey and predators. Specifically, it studies the case where prey attracts the secondary predators when threatened by the primary predators. The secondary consumers pursue the signal generated by the interaction between the prey and direct consumers. However, obtaining the necessary gradient estimates for global existence seems difficult in the critical case due to the strong coupled structure. Therefore, a new approach is developed to estimate the gradient of prey and primary predators, which takes advantage of slightly higher damping power. Subsequently, the boundedness of classical solutions in two-dimension with Neumann boundary conditions can be established by energy estimates and semigroup theory. Moreover, by constructing Lyapunov functional, it is proved that the coexistence homogeneous steady states are asymptotically stable, and the convergence rate is exponential under certain assumptions on the system coefficients.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140160182","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":"Optimal decay rates and space–time analyticity of solutions to the Patlak-Keller–Segel equations","authors":"Yu Gao ,&nbsp;Cong Wang ,&nbsp;Xiaoping Xue","doi":"10.1016/j.nonrwa.2024.104114","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104114","url":null,"abstract":"<div><p>Based on some new elementary estimates for the space–time derivatives of the heat kernel, we use a bootstrapping approach to establish quantitative estimates on the optimal decay rates for the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> (<span><math><mrow><mn>1</mn><mo>≤</mo><mi>q</mi><mo>≤</mo><mi>∞</mi></mrow></math></span>, <span><math><mrow><mi>d</mi><mo>∈</mo><mi>N</mi></mrow></math></span>) norm of the space–time derivatives of solutions to the (modified) Patlak-Keller–Segel equations with initial data in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>, which implies the joint space–time analyticity of solutions. When the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> norm of the initial datum is small, the upper bound for the decay estimates is global in time, which yields a lower bound on the growth rate of the radius of space–time analyticity in time. As a byproduct, the space analyticity is obtained for any initial data in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. The decay estimates and space–time analyticity are also established for solutions bounded in both space and time variables. The results can be extended to a more general class of equations.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140160181","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":"Ekman layer of rotating stratified viscous Boussinesq equations in rotation-dominant limit","authors":"Pengcheng Mu","doi":"10.1016/j.nonrwa.2024.104113","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104113","url":null,"abstract":"<div><p>The asymptotics of weak solutions to the Boussinesq equations with no-slip boundary and moderately ill-prepared data is investigated in rotation-dominant limit regime as the Rossby number, the Froude number and the vertical viscosity tend to zero simultaneously. The new ingredient of this paper is to give a first proof of the three scale singular limit coupled with Ekman boundary layer by introducing an asymptotic profile to the original system.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140141475","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 regularity of global attractors for a Kirchhoff wave equation with strong damping and memory","authors":"Bin Yang ,&nbsp;Yuming Qin ,&nbsp;Alain Miranville ,&nbsp;Ke Wang","doi":"10.1016/j.nonrwa.2024.104096","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104096","url":null,"abstract":"<div><p>This paper is concerned with the existence and regularity of global attractor <span><math><mi>A</mi></math></span> for a Kirchhoff wave equation with strong damping and memory in <span><math><mi>H</mi></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, respectively. In order to obtain the existence of <span><math><mi>A</mi></math></span>, we mainly use the energy method in the priori estimations, and then verify the asymptotic compactness of the semigroup by the method of contraction function. Finally, by decomposing the weak solutions into two parts and some elaborate calculations, we prove the regularity of <span><math><mi>A</mi></math></span>.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140134901","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":"On the long-time behaviour of solutions to unforced evolution Navier–Stokes equations under Navier boundary conditions","authors":"Elvise Berchio ,&nbsp;Alessio Falocchi ,&nbsp;Clara Patriarca","doi":"10.1016/j.nonrwa.2024.104102","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104102","url":null,"abstract":"<div><p>We study the asymptotic behaviour of the solutions to Navier–Stokes unforced equations under Navier boundary conditions in a wide class of merely Lipschitz domains of physical interest. The paper draws its main motivation from celebrated results by Foias and Saut (1984) under Dirichlet conditions; here the choice of the boundary conditions requires carefully considering the geometry of the domain <span><math><mi>Ω</mi></math></span>, due to the possible lack of the Poincaré inequality in presence of symmetries. In non-axially symmetric domains we show the validity of the Foias–Saut result about the limit at infinity of the Dirichlet quotient, in axially symmetric domains we provide two invariants of the flow which completely characterize the motion and we prove that the Foias–Saut result holds for initial data belonging to one of the invariants.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824000427/pdfft?md5=90d12d6bba6d4bc4f076da49b43e75f7&pid=1-s2.0-S1468121824000427-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140123132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}