This paper concerns with the motion of the interface for a damped hyperbolic Allen-Cahn equation, in a bounded domain of ℝn, for n = 2 or n = 3. In particular, we focus the attention on radially symmetric solutions and extend to the hyperbolic framework some well-known results of the classic parabolic case: it is shown that, under appropriate assumptions on the initial data and on the boundary conditions, the interface moves by mean curvature as the diffusion coefficient goes to 0.
Motion of interfaces for a damped hyperbolic Allen-Cahn equation
Lattanzio C.;
2020
Abstract
This paper concerns with the motion of the interface for a damped hyperbolic Allen-Cahn equation, in a bounded domain of ℝn, for n = 2 or n = 3. In particular, we focus the attention on radially symmetric solutions and extend to the hyperbolic framework some well-known results of the classic parabolic case: it is shown that, under appropriate assumptions on the initial data and on the boundary conditions, the interface moves by mean curvature as the diffusion coefficient goes to 0.File in questo prodotto:
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