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Author Zhu, Peicheng
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2009-12-29
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Dynamical Systems ♦ 35D ♦ 74B ♦ 35M ♦ 74N ♦ math
Abstract In the present article, we are interested in an initial boundary value problem for a coupled system of partial differential equations arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model was proposed and investigated in previous work by Alber and Zhu in which the weak solutions are defined in a standard way, however the key technique is not applicable to multi-dimensional problem. Intending to solve this multi-dimensional problem and to investigate the sharp interface limits of our models, we thus define weak solutions in a different way by using the notion of viscosity solution, then prove the existence of weak solutions to this problem in one space dimension, yet the multi-dimensional problem is still open.
Educational Use Research
Learning Resource Type Article
Page Count 21


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