Numerical verification for existence of a global-in-time solution to semilinear parabolic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:315

Article

Mizuguchi, Makoto¹  Takayasu, Akitoshi²  Kubo, Takayuki⁴  Oishi, Shin'ichi^3,5 

[1] Waseda Univ, Grad Sch Fundamental Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

[2] Univ Tsukuba, Fac Engn Informat & Syst, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058573, Japan

[3] Waseda Univ, Fac Sci & Engn, Dept Appl Math, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

[4] Univ Tsukuba, Inst Math, 1-1-1 Tennodai, Tsukuba, Ibaraki 3050006, Japan

[5] JST, CREST, Tokyo, Japan

关键词: Semilinear parabolic equations;    Global-in-time solution;    Verified numerical computations;   

DOI  :  10.1016/j.cam.2016.10.024

来源: Elsevier

【 摘 要 】

This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t = t' >= 0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t is an element of(0, iota], iota > 0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given. (C) 2016 Published by Elsevier B.V.

【 授权许可】

Free