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Viscosity solutions to a Cauchy problem of a phase‐field model for solid‐solid phase transitions
Author(s) -
Zheng Junzhi
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12325
Subject(s) - uniqueness , degenerate energy levels , mathematics , mathematical analysis , cauchy problem , initial value problem , phase transition , partial differential equation , phase (matter) , parabolic partial differential equation , principal part , curvature , physics , geometry , thermodynamics , quantum mechanics
We investigate a partial differential equation which models solid‐solid phase transitions. This model is for martensitic phase transitions driven by configurational force and its counterpart is for interface motion by mean curvature. Mathematically, this equation is a second‐order nonlinear degenerate parabolic equation. And in multidimensional case, its principal part cannot be written into divergence form . We prove the existence and uniqueness of viscosity solution to a Cauchy problem for this model.