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 coecient goes to 0.

Motion of interfaces for a damped hyperbolic Allen-Cahn equation / Folino, Raffaele; Lattanzio, Corrado; Mascia, Corrado. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1553-5258. - 19:9(2020), pp. 4507-4543. [10.3934/cpaa.2020205]

Motion of interfaces for a damped hyperbolic Allen-Cahn equation

Folino Raffaele
;
Mascia Corrado
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 coecient goes to 0.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1579497
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