Results 61 to 70 of about 357 (100)

Existence and nonexistence of global solutions of degenerate and singular parabolic systems

, 2000
Abstract and Applied Analysis, Volume 5, Issue 4, Page 265-284, 2000.
Gabriella Caristi
wiley   +1 more source

Large Time Behavior of Solutions to the Nonlinear Heat Equation with Absorption with Highly Singular Antisymmetric Initial Values

Advanced Nonlinear Studies, 2020
In this paper, we study global well-posedness and long-time asymptotic behavior of solutions to the nonlinear heat equation with absorption, ut-Δ⁢u+|u|α⁢u=0{u_{t}-\Delta u+\lvert u\rvert^{\alpha}u=0}, where u=u⁢(t,x)∈ℝ{u=u(t,x)\in\mathbb{R}}, (t,x)∈(0,∞)×
Mouajria Hattab, Tayachi Slim, Weissler Fred B.   +2 more
doaj   +1 more source

QUENCHING FOR A SEMILINEAR HEAT EQUATION WITH A SINGULAR BOUNDARY OUTFLUX

, 2016
In this paper, we study the quenching behavior of solution of a semilinear heat equation with a singular boundary outflux. We first get a local existence result for this problem.
Burhan Selçuk, N. Ozalp
semanticscholar   +1 more source

A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions

Advances in Nonlinear Analysis, 2015
A boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.
Colli Pierluigi, Gilardi Gianni, Sprekels Jürgen   +2 more
doaj   +1 more source

Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability

, 2004
Received by the editors September 18, 2002. 2000 Mathematics Subject Classification. Primary 35L60; Secondary 35B35, 35B45, 35K55, 35L65, 76L05.
O. Guès, G. Métivier, Mark E. Williams, K. Zumbrun   +3 more
semanticscholar   +1 more source

Global and non global solutions for a class of coupled parabolic systems

Advances in Nonlinear Analysis, 2020
In the present paper, we investigate the global well-posedness and exponential decay for some coupled non-linear heat equations. Moreover, we discuss the global and non global existence of solutions using the potential well method.
Saanouni T.
doaj   +1 more source

Gradient estimates for a weighted nonlinear parabolic equation and applications

Open Mathematics, 2020
This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold.
Abolarinwa Abimbola, Oladejo Nathaniel K., Salawu Sulyman O.   +2 more
doaj   +1 more source

Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks

Advances in Nonlinear Analysis
The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the ...
Li Bin
doaj   +1 more source

The nonlinear diffusion equation of the ideal barotropic gas through a porous medium

Open Mathematics, 2017
The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of ...
Zhan Huashui
doaj   +1 more source

Higher-order anisotropic models in phase separation

Advances in Nonlinear Analysis, 2017
Our aim in this paper is to study higher-order (in space) Allen–Cahn and Cahn–Hilliard models. In particular, we obtain well-posedness results, as well as the existence of the global attractor.
Cherfils Laurence, Miranville Alain, Peng Shuiran   +2 more
doaj   +1 more source