### Abstract

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.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 315 |

DOIs | |

Publication status | Published - 2017 May 1 |

### Fingerprint

### Keywords

- Global-in-time solution
- Semilinear parabolic equations
- Verified numerical computations

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

**Numerical verification for existence of a global-in-time solution to semilinear parabolic equations.** / Mizuguchi, Makoto; Takayasu, Akitoshi; Kubo, Takayuki; Oishi, Shinichi.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 315, pp. 1-16. https://doi.org/10.1016/j.cam.2016.10.024

}

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, Shinichi

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

UR - http://www.scopus.com/inward/record.url?scp=84996486884&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84996486884&partnerID=8YFLogxK

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 -