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Local well-posedness for Frémond’s model of complete damage in elastic solids

Part of: Equations and systems of special type Equations of mathematical physics and other areas of application Fracture and damage Parabolic equations and systems

Published online by Cambridge University Press:  01 March 2021

GORO AKAGI Open the ORCID record for GORO AKAGI [Opens in a new window]  and
GIULIO SCHIMPERNA Open the ORCID record for GIULIO SCHIMPERNA [Opens in a new window]
GORO AKAGI
Affiliation:
Mathematical Institute and Graduate School of Science, Tohoku University 6-3 Aoba, Aramaki, Aoba-ku, Sendai 980-8578 Japan e-mail: goro.akagi@tohoku.ac.jp
GIULIO SCHIMPERNA
Affiliation:
Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, I-27100 Pavia, Italy e-mail: giusch04@unipv.it
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Abstract

We consider a model for the evolution of damage in elastic materials originally proposed by Michel Frémond. For the corresponding PDE system, we prove existence and uniqueness of a local in time strong solution. The main novelty of our result stands in the fact that, differently from previous contributions, we assume no occurrence of any type of regularising terms.

Keywords

Degenerate elliptic–parabolic systemdamage phenomenalocal existencea priori estimates

MSC classification

Primary: 35K55: Nonlinear parabolic equations 35Q74: PDEs in connection with mechanics of deformable solids
Secondary: 35K86: Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities 35M33: Initial-boundary value problems for systems of mixed type 74R05: Brittle damage
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 2 , April 2022 , pp. 309 - 327
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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