Asymptotics of blowup for a convection-diffusion equation with conservation
type: Item
instance of: scholarly article
title: Asymptotics of blowup for a convection-diffusion equation with conservation
zbMATH Open document ID: 0856.35011
author: G. Conner
author: Christopher P. Grant
published in: Differential and Integral Equations
publication date: 1997-01-21T00:00:00Z
review text: The authors consider the following nonlinear initial-boundary value problem \[ u_t= (u_x+ u^q)_x,\text{ for }(x, t)\in (0, 1)\times (0, T),\;u_x+ u^q= 0,\text{ for }x\in \{0, 1\},\;u(x, 0)= u_0(x), \] where \(q> 2\) and \(0< T\leq \infty\). The initial function is such that finite-time blowup occurs at \(t= T\). The limiting behavior of the solution in a vicinity of the blow up point and the asymptotic growth rate are presented. In proving of these results, comparison principles are employed. For the case \(q= 3\), some numerical illustrations of theoretical results are given.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 883501
zbMATH Keywords: finite-time blow up
zbMATH Keywords: comparison principles
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 883501