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Advances in Mathematical PhysicsMSC2020 Classification: 35D30 ...
Weifeng Hu, Yunzhang Cheng
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Thermal Timoshenko beam system with suspenders and Kelvin–Voigt damping
Frontiers in Applied Mathematics and Statistics, 2023 In the present study, we consider a thermal-Timoshenko-beam system with suspenders and Kelvin–Voigt damping type, where the heat is given by Cattaneo's law. Using the existing semi-group theory and energy method, we establish the existence and uniqueness
Soh Edwin Mukiawa +4 more
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Asymptotic behaviour of the non-autonomous 3D Navier-Stokes problem with coercive force [PDF]
, 2010 We construct pullback attractors to the weak solutions of the three-dimensional Dirichlet problem for the incompressible Navier-Stokes equations in the case when the external force may become unbounded as time goes to plus or minus infinity.
Vorotnikov, Dmitry
arxiv +4 more sources
Local Continuity of Weak Solutions to the Stefan Problem Involving the Singular $p$-Laplacian [PDF]
SIAM Journal on Mathematical Analysis, 2021 We establish the local continuity of locally bounded weak solutions (temperatures) to the doubly singular parabolic equation modeling the phase transition of a material: ∂tβ(u)−∆pu 3 0 for 2N N+1 < p < 2, where β is a maximal monotone graph with a jump ...
Naian Liao
semanticscholar +1 more source
Positive solutions for (p, q)-equations with convection and a sign-changing reaction
Advances in Nonlinear Analysis, 2021 We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction which is dependent on the gradient. We look for positive solutions and we do not assume that the reaction is nonnegative.
Zeng Shengda, Papageorgiou Nikolaos S.
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Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 688-746, September 2021., 2021 Abstract This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on gradient flows in the space of probability measures equipped with the distance arising in the ...
Dohyun Kwon, Alpár Richárd Mészáros
wiley +1 more source
Boundary Value Problems, 2014 We are concerned with the following elliptic equations with variable exponents: −div(φ(x,∇u))+|u|p(x)−2u=λf(x,u) in RN, where the function φ(x,v) is of type |v|p(x)−2v with continuous function p:RN→(1,∞) and f:RN×R→R satisfies a Carathéodory condition ...
Seung Dae Lee, Kisoeb Park, Yun-Ho Kim
semanticscholar +2 more sources
A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities
Advanced Nonlinear Studies, 2023 This article deals with existence of solutions to the following fractional pp-Laplacian system of equations: (−Δp)su=∣u∣ps*−2u+γαps*∣u∣α−2u∣v∣βinΩ,(−Δp)sv=∣v∣ps*−2v+γβps*∣v∣β−2v∣u∣αinΩ,\left\{\begin{array}{l}{\left(-{\Delta }_{p})}^{s}u={| u| }^{{p}_{s}^{
Bhakta Mousomi +2 more
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Existence and nonexistence of solutions for elliptic problems with multiple critical exponents
Open Mathematics, 2023 In this article, the existence and nonexistence of solutions for the quasilinear elliptic equations involving multiple critical terms under Dirichlet boundary conditions on bounded smooth domains Ω⊂RN(N≥3)\Omega \subset {R}^{N}(N\ge 3) are proved by ...
Li Yuanyuan
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application
Advances in Nonlinear Analysis, 2020 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
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