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Global existence and blow-up for a nonlinear porous medium equation

✍ Scribed by Fucai Li; Chunhong Xie

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
405 KB
Volume
16
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this paper, we investigate the positive solution of nonlinear nonlocal porous medium equation ut -Aum = auP f~ uq dx with homogeneous Dirichlet boundary condition and positive initial value u0(x), where m > 1, p, q > 0. Under appropriate hypotheses, we establish the local existence and uniqueness of a positive classical solution, and obtain that the solution either exists globally or blows up in finite time by utilizing sub and super solution techniques. Furthermore, we yield the blow-up rate, i.e., there exist two positive constants C1, C2 such that

where p + q > m > 1, T* is the blow-up time of u(x,t).

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✍ Salim A. Messaoudi πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 133 KB πŸ‘ 1 views

## Abstract In this paper the nonlinear viscoelastic wave equation associated with initial and Dirichlet boundary conditions is considered. Under suitable conditions on __g__, it is proved that any weak solution with negative initial energy blows up in finite time if __p__ > __m__. Also the case o