We consider a class of parabolic partial differential equations with nonlocal diffusion coefficient. The study is motivated by a model of turbulent viscosity for a developed flow in a duct between parallel walls. Under rather more general conditions, we use a rescaling in t to prove existence and we
On a semilinear parabolic equation arising in optical bistability
β Scribed by K.J Brown; A Tertikas
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 831 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
In this paper, we investigate initial boundary value problems for semilinear parabolic differential equations with singular term. A criterion for the appearance of quencing phenomena of classical solution to the above problems on a bounded domain is given and a global existence and nonexistence resu
This paper studies the problem ¨s d¨q ¨q y 1 y cos x ¨p , for 0x -1 and t ) 0, Ž . for x s 0, 1 and t ) 0, x ¨x, 0 s ¨x , for 0x -1, ## Ž . Ž . 0 where 1qp, d ) 0. It is shown that for large initial data if p -2 q y 1 or p s 2q y 1 but d is small, then the positive solution blows up in finite t