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- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-010-9563-9
- Publisher site
- See Article on Publisher Site
Abstract
This paper deals with a class of localized and degenerate quasilinear parabolic systems $$u_t=f(u)(\Delta u+av(x_0,t)),\qquad v_t=g(v)(\Delta v+bu(x_0,t))$$ with homogeneous Dirichlet boundary conditions. Local existence of positive classical solutions is proven by using the method of regularization. Global existence and blow-up criteria are also obtained. Moreover, the authors prove that under certain conditions, the solutions have global blow-up property.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Feb 5, 2010