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Blow-up solutions for a class of nonlinear parabolic equations with Dirichlet boundary conditions

✍ Scribed by Juntang Ding

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
119 KB
Volume
52
Category
Article
ISSN
0362-546X

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✦ Synopsis

In the present paper, the blow up of smooth local solutions for a class of nonlinear parabolic equations u;t =βˆ‡(a(u)βˆ‡u) + f(x; u; q; t) (q = |βˆ‡u| 2 ) with Dirichlet boundary conditions are studied. By constructing an auxiliary function and using Hopf's maximum principles on it, the su cient conditions for blow-up solutions are obtained and the upper bound of "blow-up time" is given under some suitable assumptions on a; f and initial date. The obtained results are applied to some examples in which a and f are exponential functions.

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