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The Cauchy problem for a coupled semilinear parabolic system

✍ Scribed by L. Amour; T. Raoux

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

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✦ Synopsis

We consider a semilinear parabolic coupled system

in R n Γ— R+ where the maximum principle and the minimum principle fail for the solution itself and also for its ΓΏrst derivatives with respect to x. Under the assumption that f and g present a subquadratic growth near the origin, we prove the global existence and uniqueness of the solutions to the Cauchy problem, and the existence of nonnegative solutions. The maximum principle and the minimum principle are replaced by the existence of some invariant regions in R 2n+2 for

πŸ“œ SIMILAR VOLUMES

Blow-up estimates for a semilinear coupl
Blow-up estimates for a semilinear coupled parabolic system
✍ Gang Li; Ping Fan; Jiang Zhu πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 424 KB

This work deals with a semilinear parabolic system which is coupled both in the equations and in the boundary conditions. The blow-up phenomena of its positive solutions are studied using the scaling method, the Green function and Schauder estimates. The upper and lower bounds of blow-up rates are t