TY - JOUR

T1 - Numerical verification for existence of a global-in-time solution to semilinear parabolic equations

AU - Mizuguchi, Makoto

AU - Takayasu, Akitoshi

AU - Kubo, Takayuki

AU - Oishi, Shin'ichi

N1 - Funding Information:
The authors express their sincere thanks to Prof. Masahide Kashiwagi in Waseda University, Assoc. Prof. Takuma Kimura in Saga University, Asst. Prof. Kouta Sekine, and Mr. Kazuaki Tanaka in Waseda University for their useful comments. The authors also would like to express sincere thanks to anonymous referees for giving them useful comments to improve this paper. The third author was supported in part by Grant for Basic Science Research Projects from The Sumitomo Foundation ( 121039 ).

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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∈(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.

AB - 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∈(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.

KW - Global-in-time solution

KW - Semilinear parabolic equations

KW - Verified numerical computations

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U2 - 10.1016/j.cam.2016.10.024

DO - 10.1016/j.cam.2016.10.024

M3 - Article

AN - SCOPUS:84996486884

VL - 315

SP - 1

EP - 16

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -