Numerical existence and uniqueness proof for solutions of semilinear parabolic equations
✍ Scribed by T. Minamoto
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 466 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
Communicated by H. J. Stetter
Abstract-we describe a numerical method to verify the existence and local uniqueness of solutions of semilinear parabolic equations. We present a detailed description of the verification procedure and determine error bounds for its computation. Several examples are given.
📜 SIMILAR VOLUMES
Existence theorems for the nonlinear parabolic differential equation yѨ urѨ t q < < p Ž . n w . ⌬uq u qf x, t s 0 in ޒ = 0, ϱ with zero initial value are established given Ž . explicit conditions on the nonhomogeneous term f x, t . An existence theorem is also demonstrated for the corresponding e
## Abstract Theoretical aspects related to the approximation of the semilinear parabolic equation: $u\_t=\Delta u+f(u)$\nopagenumbers\end, with a finite unknown ‘blow‐up’ time __T__~b~ have been studied in a previous work. Specifically, for __ε__ a small positive number, we have considered coupled