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A new proof of the existence of weak solutions to a model for phase evolution driven by material forces
Author(s) -
Tang Yangxin,
Wang Wenhua,
Zhou Yu
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4354
Subject(s) - mathematics , nonlinear system , mathematical analysis , boundary value problem , weak solution , elasticity (physics) , partial differential equation , work (physics) , function (biology) , weak formulation , physics , quantum mechanics , evolutionary biology , biology , thermodynamics
We prove the existence of weak solutions to a one‐dimensional initial‐boundary value problem for a model system of partial differential equations, which consists of a sub‐system of linear elasticity and a nonlinear non‐uniformly parabolic equation of second order. To simplify the existence proof of weak solutions in the 2006 paper of Alber and Zhu, we replace the function | p | κ : = | p | 2 / | p | 2 + κ 2in that work by | p | κ : = | p | 2 + κ 2. The model is formulated by using a sharp interface model for phase transformations that are driven by material forces. Copyright © 2017 John Wiley & Sons, Ltd.