The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (107 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 25, Issue 4, 2006, pp. 479–486
DOI: 10.4171/ZAA/1303

Published online: 2006-12-31

Blow-up of Solutions for a Class of Nonlinear Parabolic Equations

Zhang Lingling[1]

(1) Taiyuan University of Technology, China

In this paper, the blow up of solutions for a class of nonlinear parabolic equations $$ u_t(x,t)=\nabla _{x}(a(u(x,t))b(x)c(t)\nabla _{x}u(x,t))+g(x,|\nabla _{x}u(x,t) |^2,t)f(u(x,t)) $$ with mixed boundary conditions is studied. By constructing an auxiliary function and using Hopf's maximum principles, an existence theorem of blow-up solutions, upper bound of ``blow-up time" and upper estimates of ``blow-up rate" are given under suitable assumptions on $a, b,c, f, g$, initial data and suitable mixed boundary conditions. The obtained result is illustrated through an example in which $a, b,c, f, g$ are power functions or exponential functions.

Keywords: Nonlinear parabolic equations, blow-up solutions, maximum principles

Lingling Zhang: Blow-up of Solutions for a Class of Nonlinear Parabolic Equations. Z. Anal. Anwend. 25 (2006), 479-486. doi: 10.4171/ZAA/1303