Viscosity solutions to a Cauchy problem of a phase‐field model for solid‐solid phase transitions. Issue 3 (9th July 2020)

• Record Type: Journal Article
• Authors: Zheng, Junzhi
• Is Part Of: Studies in applied mathematics. Volume 145:Issue 3(2020)
• Page Start: 483
• Page End: 499
• Publication Date: 2020-07-09
• Subjects: Cauchy problem -- configurational forces -- nonlinear degenerate parabolic equation -- phase‐field model -- viscosity solution; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12325
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: 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.