We consider the initial-boundary value problem of some semi-linear parabolic equations with superlinear and subcritical nonlinear terms. In this paper, we consider global solutions, which could be sign changing, and estimate the dependence of upper bounds of global solutions on some norm of the init
A critical behavior for some semilinear parabolic equations involving sign changing solutions
โ Scribed by Qi S. Zhang
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 110 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The blowup of solutions of the Cauchy problem { u t =u xx + |u| p&1 u u(x, 0)=u 0 (x) in R\\_(0, ), in R is studied. Let 4 k be the set of functions on R which change sign k times. It is shown that for p k =1+2ร(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T
0 with the Dirichlet, Neumann, or periodic boundary condition. Here ) 0 is a ลฝ . parameter, and f is an odd function of u satisfying f ะ 0 ) 0 and some convexity ลฝ . w x condition. Let z U be the number of times of sign changes for U g C 0, 1 . It is ร 4 shown that there exists an increasing sequenc
We use the mountain pass theorem to study the existence and multiplicity of positive solutions of the generalisation of the well-known logistic equation -u = g(x)u(x)(1 -u(x)) with Dirichlet boundary conditions to the case where g changes sign.