Unidirectional evolution equations of diffusion type
| Autor: | Goro Akagi, Masato Kimura |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Diffusion equation
Discretization Applied Mathematics 010102 general mathematics 01 natural sciences Backward Euler method 35K86 35K61 74A45 010101 applied mathematics Mathematics - Analysis of PDEs Unidirectional Diffusion Equation Damage Mechanics Variational Inequality Of Obstacle Type Regularity Subdifferential Calculus Damage mechanics Variational inequality FOS: Mathematics Applied mathematics Uniqueness 0101 mathematics Reduction (mathematics) Analysis Smoothing Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | J. Differ. Equations 266, 1-43 (2019) |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2018.05.022 |
| Popis: | This paper is concerned with the uniqueness, existence, partial smoothing effect, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of solutions is proved in an L-2-framework by employing a backward Euler scheme and by introducing a new method of a priori estimates based on a reduction of discretized equations to variational inequalities of obstacle type and by developing a regularity theory for such obstacle problems. The novel discretization argument will be also applied to prove the comparison principle as well as to investigate the long-time behavior of solutions. (C) 2018 Elsevier Inc. All rights reserved. |
| Databáze: | OpenAIRE |
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