Calculus of Variations and Geometric Measure Theory
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M. Bonafini - V. P. C. Le - M. Novaga - G. Orlandi

On the obstacle problem for fractional semilinear wave equations

created by le on 04 Nov 2020
modified on 05 Nov 2020

[BibTeX]

Submitted Paper

Inserted: 4 nov 2020
Last Updated: 5 nov 2020

Pages: 23
Year: 2020
Links: Paper on the obstacle problem for fractional semilinear wave equations

Abstract:

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in 8, where the linear case was treated. In addition, we deduce some compactness properties of concentration sets (e.g. moving interfaces) when dealing with singular limits of certain nonlinear wave equations.

Keywords: minimizing movements, Hyperbolic obstacle problem, Non-local nonlinear wave equations, Singular limits


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