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Article

Zhu, Peicheng
Spherically symmetric solutions to a model for interface motion by interface diffusion. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 240-247
MSC: 35B07, 35K41, 35K46, 35M33, 35Q74, 74N15, 80A22, 82C24, 82C26 | MR 3204448 | Zbl 1340.35114
Keywords:
quasi-static process; initial-boundary value problem; a priori estimate; Egorov theorem; spherically symmetric solution
Summary:
The existence of spherically symmetric solutions is proved for a new phase-field model that describes the motion of an interface in an elastically deformable solid, here the motion is driven by configurational forces. The model is an elliptic-parabolic coupled system which consists of a linear elasticity system and a non-linear evolution equation of the order parameter. The non-linear equation is non-uniformly parabolic and is of fourth order. One typical application is sintering.
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