Verified computations for solutions to semilinear parabolic equations using the evolution operator

Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shinichi Oishi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This article presents a theorem for guaranteeing existence of a solution for an initial-boundary value problem of semilinear parabolic equations. The sufficient condition of our main theorem is derived by a fixed-point formulation using the evolution operator. We note that the sufficient condition can be checked by verified numerical computations.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages218-223
Number of pages6
Volume9582
ISBN (Print)9783319328584
DOIs
Publication statusPublished - 2016
Event6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany
Duration: 2015 Nov 112015 Nov 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9582
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015
CountryGermany
CityBerlin
Period15/11/1115/11/13

Fingerprint

Semilinear Parabolic Equation
Evolution Operator
Boundary value problems
Sufficient Conditions
Theorem
Numerical Computation
Initial-boundary-value Problem
Fixed point
Formulation

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Takayasu, A., Mizuguchi, M., Kubo, T., & Oishi, S. (2016). Verified computations for solutions to semilinear parabolic equations using the evolution operator. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9582, pp. 218-223). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582). Springer Verlag. https://doi.org/10.1007/978-3-319-32859-1_18

Verified computations for solutions to semilinear parabolic equations using the evolution operator. / Takayasu, Akitoshi; Mizuguchi, Makoto; Kubo, Takayuki; Oishi, Shinichi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9582 Springer Verlag, 2016. p. 218-223 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Takayasu, A, Mizuguchi, M, Kubo, T & Oishi, S 2016, Verified computations for solutions to semilinear parabolic equations using the evolution operator. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 9582, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9582, Springer Verlag, pp. 218-223, 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, Berlin, Germany, 15/11/11. https://doi.org/10.1007/978-3-319-32859-1_18
Takayasu A, Mizuguchi M, Kubo T, Oishi S. Verified computations for solutions to semilinear parabolic equations using the evolution operator. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9582. Springer Verlag. 2016. p. 218-223. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-32859-1_18
Takayasu, Akitoshi ; Mizuguchi, Makoto ; Kubo, Takayuki ; Oishi, Shinichi. / Verified computations for solutions to semilinear parabolic equations using the evolution operator. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9582 Springer Verlag, 2016. pp. 218-223 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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