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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 52

Weak Solution to KWC Systems of Pseudo-parabolic Type

Author(s)
Daiki Mizuno1

1Chiba University, Chiba, Japan

Abstract
In this paper, a class of systems of pseudo-parabolic PDEs is considered. These systems (S)ε are derived as a pseudo-parabolic dissipation system of Kobayashi– Warren–Carter energy, proposed by [Kobayashi et al., Physica D, 140, 141–150 (2000)], to describe planar grain boundary motion. In this context, ε is a value to control the relaxation of singular diffusivity. These systems have been studied in [Antil et al., SIAM J. Math. Anal., 56(5), 6422–6455], and solvability, uniqueness and strong regularity of the solution have been reported under the setting that the initial data is sufficiently smooth. Meanwhile, in this paper, we impose weaker regularity on the initial data, and work on the weak formulation of the systems. In this light, we set our goal of this paper to prove two theorems, concerned with the existence and the uniqueness of weak solution to (S)ε, and the continuous dependence with respect to the index ε, initial data and forcings.
About the Authors
Daiki Mizuno, Postgraduate, Chiba University, Chiba, 263-8522, Japan, d-mizuno@chiba-u.jp
For citation
Mizuno D. Weak Solution to KWC Systems of Pseudo-parabolic Type. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 52, pp. 88–104.

https://doi.org/10.26516/1997-7670.2025.52.88

Keywords
planar grain boundary motion, pseudo-parabolic KWC system, energydissipation, singular diffusion, time-discretization
UDC
517.9
MSC
35G61, 35J57, 35J62, 35K70, 74N20
DOI
https://doi.org/10.26516/1997-7670.2025.52.88
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