The uniqueness of nonnegative \(C^{1}\)-solution for nonlinear differential equations
type: Item
instance of: scholarly article
title: The uniqueness of nonnegative \(C^{1}\)-solution for nonlinear differential equations
zbMATH Open document ID: 1058.35094
DOI: 10.1016/S0096-3003(03)00643-X
author: Shuxia Han
author: Zhiwen Duan
author: Li Zhou
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: This paper is devoted to a study of the nonlinear degenerate parabolic system \[ \begin{cases} u_t= u^{\alpha_1}(u_{xx}+ av),\quad & x\in(-\ell,\ell),\;0< t< T,\\ v_t= v^{\alpha_2}(v_{xx}+ bu),\quad & x\in(-\ell,\ell),\;0< t< T,\\ u(\pm\ell, t)= v(\pm\ell, t)= 0,\quad & 0< t< T,\end{cases}\tag{1} \] where \(\alpha_1\), \(\alpha_2\), \(a\), \(b> 0\) are constants. For (1) the authors estimate the blow up rate and analyze the asymptotic behaviour of the blow up solution near the blow up time. Uniqueness and some numerical results are presented.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2082061
zbMATH Keywords: degenerate parabolic system
zbMATH Keywords: blow up rate
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3221003
cites work: Q3733325
cites work: Global and blow‐up solutions for non‐linear degenerate parabolic systems
cites work: Analysis of blowup for a nonlinear degenerate parabolic equation
cites work: On Asymptotic Self-Similar Behaviour for a Quasilinear Heat Equation: Single Point Blow-Up
cites work: Stabilization of solutions of a degenerate nonlinear diffusion problem
full work available at URL: s0096-3003(03)00643-x
OpenAlex ID: W1998630865
description: scientific article; zbMATH DE number 2082061