A new proof of the existence of weak solutions to a model for phase evolution driven by material forces | Zendy

Tang Yangxin | Zendy; Wang Wenhua | Zendy; Zhou Yu | Zendy

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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.

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