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

详细信息    查看全文

• 作者：Makoto Mizuguchi^a ; ^{makoto.math@fuji.waseda.jp} ; Akitoshi Takayasu^b ; ^{takitoshi@risk.tsukuba.ac.jp} ; Takayuki Kubo^d ; ^{tkubo@math.tsukuba.ac.jp} ; Shin'ichi Oishi^c ; ^e ; ^{oishi@waseda.jp}
• 关键词：65G40 ; 65M15 ; 35K20
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：315
• 期：Complete
• 页码：1-16
• 全文大小：1588 K
• 卷排序：315

文摘

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′≥0t=t′≥0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t∈(0,τ],τ>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.