In this paper, the blow up of solutions for a class of nonlinear parabolic equations
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 , initial data and suitable mixed boundary conditions. The obtained result is illustrated through an example in which are power functions or exponential functions.
Cite this article
Zhang Lingling, Blow-up of Solutions for a Class of Nonlinear Parabolic Equations. Z. Anal. Anwend. 25 (2006), no. 4, pp. 479–486DOI 10.4171/ZAA/1303