Regularity of solutions to a model for solid-solid phase transitions driven by configurational forces
In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with H 1(Ω) initial data, for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, degenerate parabolic equation of second order. This probl...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/579 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/579 |
| Access Level: | acceso abierto |
| Palabra clave: | Degenerate parabolic equation Phase transition model Regularity Weak solutions |
| Sumario: | In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with H 1(Ω) initial data, for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, degenerate parabolic equation of second order. This problem models the behavior in time of materials with martensitic phase transitions. This model with diffusive phase interfaces was derived from a model with sharp interfaces, whose evolution is driven by configurational forces, and can be regarded as a regularization of that model. Assuming in this article the initial data is in H 2(Ω), we investigate the regularity of weak solutions that is difficult due to the gradient term which plays a role of a weight. Our proof, in which the difficulties are caused by the weight in the principle term, is only valid in one space dimension. |
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