Reaction diffusion equations with non-linear boundary conditions, blowup and steady states
✍ Scribed by Anthony W. Leung; Qin Zhang
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 186 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
where L1, is a smooth bounded domain, f and g are smooth functions which are positive when the argument is positive, and u (x)'0 satisfies some smooth and compatibility conditions to guarantee the classical solution u(x, t) exists. We first obtain some existence and non-existence results for the corresponding elliptic problems. Then, we establish certain conditions for a finite time blow-up and global boundedness of the solutions of the time-dependent problem. Further, we analyse systems with same kind of boundary conditions and find some blow-up results. In the last section, we study the corresponding elliptic problems in one-dimensional domain. Our main method is the comparison principle and the construction of special forms of upper-lower solutions using related equations.