Damped cubic wave equation on bounded domains
Published on:
19 October 2023
Primary Category:
Analysis of PDEs
Paper Authors:
Thomas Perrin
Bullets
Key Details
With damping, dichotomy between global existence and blowup below ground state energy still holds
With geometric control damping, solutions below ground state energy can be stabilized
Any bounded global solution converges to a stationary solution along some time sequence
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Damped cubic wave equation on bounded domains
This paper studies the focusing cubic wave equation with damping on a 3D compact Riemannian manifold. It proves that with damping, the dichotomy between global existence and blowup below the ground state energy still holds. With geometric control damping, solutions below the ground state energy can be stabilized, and any bounded global solution converges to a stationary solution along a sequence of times.
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