Solutions to a Model with Nonuniformly Parabolic Terms for Phase Evolution Driven by Configurational Forces
Solutions to a Model with Nonuniformly Parabolic Terms for Phase Evolution Driven by Configurational Forces
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DOI：
10.1137/050629951
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发表时间：
2005
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影响因子：
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通讯作者：
H. Alber;P. Zhu
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文献类型：
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作者：
H. Alber;P. Zhu
本文证明了一类由线性弹性力学方程和二阶非线性非一致抛物型方程组成的偏微分方程组的初边值问题在时间上整体解的存在性。该问题模拟了具有马氏体相变的材料在时间上的行为。这个模型与扩散相界面是从一个模型与尖锐的界面，其演变是由配置力驱动，可以被认为是该模型的正则化。我们的存在性证明，这有助于验证的模型，只在一维空间有效。
We prove the existence of solutions global in time to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear nonuniformly parabolic equation of second order. The problem models the behavior in time of materials with martensitic phase transformations. This model with diffusive phase interfaces was derived from a model with sharp interfaces, whose evolution is driven by configurational forces, and can be considered to be a regularization of that model. Our existence proof, which contributes to the verification of the model, is only valid in one space dimension.