Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel","authors":"Debora Amadori ,&nbsp;Cleopatra Christoforou","doi":"10.1016/j.na.2024.113576","DOIUrl":"https://doi.org/10.1016/j.na.2024.113576","url":null,"abstract":"<div><p>We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in Amadori and Christoforou (2022) to the Cauchy problem for any <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24000956/pdfft?md5=6a93db7ec31a9b1dcb1acab286d942f3&pid=1-s2.0-S0362546X24000956-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141090377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The anisotropic convexity of domains and the boundary estimate for two Monge–Ampère equations","authors":"Ruosi Chen ,&nbsp;Huaiyu Jian","doi":"10.1016/j.na.2024.113580","DOIUrl":"https://doi.org/10.1016/j.na.2024.113580","url":null,"abstract":"<div><p>We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge–Ampère Equations: one is singular which is from the proper affine hyperspheres with constant mean curvature; the other is degenerate which is from the Monge–Ampère eigenvalue problem. As a result, we obtain the sharp boundary estimates and the optimal global Hölder regularity for the two equations.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141090378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Periodic fractional Ambrosetti–Prodi for one-dimensional problem with drift","authors":"B. Barrios ,&nbsp;L. Carrero ,&nbsp;A. Quass","doi":"10.1016/j.na.2024.113563","DOIUrl":"https://doi.org/10.1016/j.na.2024.113563","url":null,"abstract":"<div><p>We prove Ambrosetti–Prodi type results for periodic solutions of some one-dimensional nonlinear problems that can have drift term whose principal operator is the fractional Laplacian of order <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. We establish conditions for the existence and nonexistence of solutions of those problems. The proofs of the existence results are based on the sub-supersolution method combined with topological degree type arguments. We also obtain a priori bounds in order to get multiplicity results. We also prove that the solutions are <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> under some regularity assumptions in the nonlinearities, that is, the solutions of the mentioned equations are classical. We finish the work obtaining Ambrosetti-Prodi-type results for a problem with singular nonlinearities.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141083919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Positive and sign-changing stationary solutions of degenerate logistic type equations","authors":"Maristela Cardoso ,&nbsp;Flávia Furtado ,&nbsp;Liliane Maia","doi":"10.1016/j.na.2024.113575","DOIUrl":"https://doi.org/10.1016/j.na.2024.113575","url":null,"abstract":"<div><p>In this work we study the existence and uniqueness of a positive, as well as a sign-changing steady-state solution of the degenerate logistic equation with a non-homogeneous superlinear term. Our outcome on a solution that changes sign, defined in higher dimensions, contribute to the existing literature of a few results for the problem, mostly developed in one dimension. We apply variational techniques, in particular the problem constrained to the Nehari manifold, and investigate how it changes as the parameter <span><math><mi>λ</mi></math></span> in the equation or the function <span><math><mi>b</mi></math></span> vary, affecting the existence and non-existence of solutions of the elliptic problem.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141072754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinite transition solutions for an Allen–Cahn equation","authors":"Wen-Long Li","doi":"10.1016/j.na.2024.113572","DOIUrl":"https://doi.org/10.1016/j.na.2024.113572","url":null,"abstract":"<div><p>We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen–Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141072722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation, regularity and positivity preservation on Riemannian manifolds","authors":"Stefano Pigola,&nbsp;Daniele Valtorta,&nbsp;Giona Veronelli","doi":"10.1016/j.na.2024.113570","DOIUrl":"https://doi.org/10.1016/j.na.2024.113570","url":null,"abstract":"<div><p>The paper focuses on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-Positivity Preservation property (<span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-PP for short) on a Riemannian manifold <span><math><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></mrow></math></span>. It states that any <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> function <span><math><mi>u</mi></math></span> with <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>+</mo><mi>∞</mi></mrow></math></span>, which solves <span><math><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>u</mi><mo>≥</mo><mn>0</mn></mrow></math></span> on <span><math><mi>M</mi></math></span> in the sense of distributions must be non-negative. Our main result is that the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-PP holds if (the possibly incomplete) <span><math><mi>M</mi></math></span> has a finite number of ends with respect to some compact domain, each of which is <span><math><mi>q</mi></math></span>-parabolic for some, possibly different, values <span><math><mrow><mn>2</mn><mi>p</mi><mo>/</mo><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>&lt;</mo><mi>q</mi><mo>≤</mo><mo>+</mo><mi>∞</mi></mrow></math></span>. When <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>, since <span><math><mi>∞</mi></math></span>-parabolicity coincides with geodesic completeness, our result settles in the affirmative a conjecture by M. Braverman, O. Milatovic and M. Shubin in 2002. On the other hand, we also show that the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-PP is stable by removing from a complete manifold a possibly singular set with Hausdorff co-dimension strictly larger than <span><math><mrow><mn>2</mn><mi>p</mi><mo>/</mo><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> or with a uniform Minkowski-type upper estimate of order <span><math><mrow><mn>2</mn><mi>p</mi><mo>/</mo><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. The threshold value <span><math><mrow><mn>2</mn><mi>p</mi><mo>/</mo><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is sharp as we show that when the Hausdorff co-dimension of the removed set is strictly smaller, then the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-PP fails. This gives a rather complete picture. The tools developed to carry out our investigations include smooth monotonic approximation and consequent regularity results for subharmonic distributions, a manifold version of the Brezis–Kato inequality, Liouville-type theorems in low regularity, removable singularities results for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141068219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 for solutions of quasilinear degenerate elliptic systems","authors":"Patrizia Di Gironimo ,&nbsp;Francesco Leonetti ,&nbsp;Marta Macrì","doi":"10.1016/j.na.2024.113562","DOIUrl":"https://doi.org/10.1016/j.na.2024.113562","url":null,"abstract":"<div><p>The existence of a solution to a quasilinear system of degenerate equations is proved, assuming that the datum has an intermediate degree of summability and that the off-diagonal coefficients have a support contained in a crossed staircase set. The support required in this paper is larger than the one assumed in a previous work.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140952376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unsteady non-Newtonian fluid flows with boundary conditions of friction type: The case of shear thinning fluids","authors":"Mahdi Boukrouche ,&nbsp;Hanene Debbiche ,&nbsp;Laetitia Paoli","doi":"10.1016/j.na.2024.113555","DOIUrl":"https://doi.org/10.1016/j.na.2024.113555","url":null,"abstract":"<div><p>Following the previous part of our study on unsteady non-Newtonian fluid flows with boundary conditions of friction type we consider in this paper the case of pseudo-plastic (shear thinning) fluids. The problem is described by a <span><math><mi>p</mi></math></span>-Laplacian non-stationary Stokes system with <span><math><mrow><mi>p</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span> and we assume that the fluid is subjected to mixed boundary conditions, namely non-homogeneous Dirichlet boundary conditions on a part of the boundary and a slip fluid-solid interface law of friction type on another part of the boundary. Hence the fluid velocity should belong to a subspace of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><mrow><mo>(</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><msup><mrow><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>Ω</mi></math></span> is the flow domain and <span><math><mrow><mi>T</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, and satisfy a non-linear parabolic variational inequality. In order to solve this problem we introduce first a vanishing viscosity technique which allows us to consider an auxiliary problem formulated in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msup><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><mrow><mo>(</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msup><msup><mrow><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>&gt;</mo><mn>2</mn></mrow></math></span> the conjugate number of <span><math><mi>p</mi></math></span> and to use the existence results already established in Boukrouche et al. (2020). Then we apply both compactness arguments and a fixed point method to prove the existence of a solution to our original fluid flow problem.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140918381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fick’s law selects the Neumann boundary condition","authors":"Danielle Hilhorst ,&nbsp;Seung-Min Kang ,&nbsp;Ho-Youn Kim ,&nbsp;Yong-Jung Kim","doi":"10.1016/j.na.2024.113561","DOIUrl":"https://doi.org/10.1016/j.na.2024.113561","url":null,"abstract":"<div><p>We show that the Neumann boundary condition appears along the boundary of an inner domain when the diffusivity of the outer domain goes to zero. We take Fick’s diffusion law with a bistable reaction function, and the diffusivity is 1 in the inner domain and <span><math><mrow><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> in the outer domain. The convergence of the solution as <span><math><mrow><mi>ϵ</mi><mo>→</mo><mn>0</mn></mrow></math></span> is shown, where the limit satisfies the Neumann boundary condition along the boundary of an inner domain. This observation says that the Neumann boundary condition is a natural choice of boundary conditions when Fick’s diffusion law is taken.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140914034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 persistence of multiplicity of eigenvalues of fractional Laplacian under perturbations","authors":"Marco Ghimenti ,&nbsp;Anna Maria Micheletti ,&nbsp;Angela Pistoia","doi":"10.1016/j.na.2024.113558","DOIUrl":"https://doi.org/10.1016/j.na.2024.113558","url":null,"abstract":"<div><p>We consider the eigenvalue problem for the fractional Laplacian <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></math></span>, <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, in a bounded domain <span><math><mi>Ω</mi></math></span> with Dirichlet boundary condition. A recent result (see Fall et al., 2023) states that, under generic small perturbations of the coefficient of the equation or of the domain <span><math><mi>Ω</mi></math></span>, all the eigenvalues are simple. In this paper we give a condition for which a perturbation of the coefficient or of the domain preserves the multiplicity of a given eigenvalue. Also, in the case of an eigenvalue of multiplicity <span><math><mrow><mi>ν</mi><mo>=</mo><mn>2</mn></mrow></math></span> we prove that the set of perturbations of the coefficients which preserve the multiplicity is a smooth manifold of codimension 2 in <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140906180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}