Name
Title | ||
|---|---|---|
A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory. |
Abstract | ||
|---|---|---|
This paper presents a numerical method for verifying the existence and local uniqueness of a solution for an initial-boundary value problem of semilinear parabolic equations. The main theorem of this paper provides a sufficient condition for a unique solution to be enclosed within a neighborhood of a numerical solution. In the formulation used in this paper, the initial-boundary value problem is transformed into a fixed-point form using an analytic semigroup. The sufficient condition is derived from Banach's fixed-point theorem. This paper also introduces a recursive scheme to extend a time interval in which the validity of the solution can be verified. As an application of this method, the existence of a global-in-time solution is demonstrated for a certain semilinear parabolic equation. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/141001664 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
semilinear parabolic initial-boundary value problems,verified numerical computations,existence and local uniqueness | Parabolic partial differential equation,Uniqueness,Mathematical optimization,Mathematical analysis,Analytic semigroup,Numerical analysis,Semigroup,Recursion,Mathematics,Parabola,Computation | Journal |
Volume | Issue | ISSN |
55 | 2 | 0036-1429 |
Citations | PageRank | References |
1 | 0.37 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Makoto Mizuguchi | 1 | 6 | 1.66 |
| Akitoshi Takayasu | 2 | 7 | 1.70 |
| Kubo, Takayuki | 3 | 1 | 0.71 |
| Shin'ichi Oishi | 4 | 280 | 37.14 |