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May/June 2015 Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
Anton Savostianov
Adv. Differential Equations 20(5/6): 495-530 (May/June 2015).

Abstract

The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping term of the form $(-{\Delta_x})^\alpha{\partial_t}u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\mathbb R^3$. It appears that to prove well-posedness and develop smooth attractor theory for the problem, we need additional regularity of the solutions, which does not follow from the energy estimate. Considering the original problem as perturbation of the linear one the task is reduced to derivation of Strichartz type estimate for the linear wave equation with fractional damping, which is the main feature of the work. Existence of smooth exponential attractor for the natural dynamical system associated with the problem is also established.

Citation

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Anton Savostianov. "Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains." Adv. Differential Equations 20 (5/6) 495 - 530, May/June 2015.

Information

Published: May/June 2015
First available in Project Euclid: 30 March 2015

zbMATH: 1316.35047
MathSciNet: MR3327705

Subjects:
Primary: 35B40, 35B45, 35L70

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 5/6 • May/June 2015
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