Results 1 to 10 of about 152 (41)
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
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Advanced Nonlinear Studies, 2021 The purpose of the article is to study the existence, regularity, stabilization and blow-up results of weak solution to the following parabolic (p,q){(p,q)}-singular equation:
Giacomoni Jacques +2 more
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Blow-up results of the positive solution for a class of degenerate parabolic equations
Open Mathematics, 2021 This paper is devoted to discussing the blow-up problem of the positive solution of the following degenerate parabolic equations: (r(u))t=div(∣∇u∣p∇u)+f(x,t,u,∣∇u∣2),(x,t)∈D×(0,T∗),∂u∂ν+σu=0,(x,t)∈∂D×(0,T∗),u(x,0)=u0(x),x∈D¯.\left\{\begin{array}{ll}{(r ...
Dong Chenyu, Ding Juntang
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On the local behavior of local weak solutions to some singular anisotropic elliptic equations
Advances in Nonlinear Analysis, 2022 We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\
Ciani Simone +2 more
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Regularity of solutions of the parabolic normalized p-Laplace equation
Advances in Nonlinear Analysis, 2018 The parabolic normalized p-Laplace equation is studied. We prove that a viscosity solution has a time derivative in the sense of Sobolev belonging locally to L2{L^{2}}.
Høeg Fredrik Arbo, Lindqvist Peter
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A Picone identity for variable exponent operators and applications
Advances in Nonlinear Analysis, 2019 In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u).
Arora Rakesh +2 more
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Stability of constant steady states of a chemotaxis model [PDF]
arXiv, 2021 The Cauchy problem for the parabolic--elliptic Keller--Segel system in the whole $n$-dimensional space is studied. For this model, every constant $A \in \mathbb{R}$ is a stationary solution. The main goal of this work is to show that $A < 1$ is a stable steady state while $A > 1$ is unstable.
arxiv
Existence of mild solutions for a singular parabolic equation and stabilization
Advances in Nonlinear Analysis, 2015 In this paper, we study the existence and the uniqueness of a positive mild solution for the following singular nonlinear problem with homogeneous Dirichlet boundary conditions: (St) ∂tu - Δpu = u -δ + f(x,u) in (0,T) × Ω =: QT, u = 0 on (0,T) × ∂Ω, u ...
Bougherara Brahim, Giacomoni Jacques
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Extinction for a Singular Diffusion Equation with Strong Gradient Absorption Revisited
Advanced Nonlinear Studies, 2018 When 2N/(N+1)
Iagar Razvan Gabriel +1 more
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Hölder gradient estimates for a class of singular or degenerate parabolic equations
Advances in Nonlinear Analysis, 2017 We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril +2 more
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