Global existence results for semi-linear structurally damped wave equations with nonlinear convection

Autor:	Tuan Anh Dao, Hiroshi Takeda
Rok vydání:	2021
Předmět:	Physics Nonlinear system Small data General Mathematics Mathematical analysis Principal part Initial value problem Damped wave Diffusion (business) Wave equation Constant (mathematics) Analysis
Zdroj:	Journal of Hyperbolic Differential Equations. 18:729-760
ISSN:	1793-6993 0219-8916
DOI:	10.1142/s0219891621500223
Popis:	In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term [Formula: see text], where [Formula: see text] is a constant. As is now well known, the linear principal part brings both the diffusion phenomenon and the regularity loss of solutions. This implies that, for the nonlinear problems, the choice of solution spaces plays an important role to obtain the global solutions with the sharp decay properties in time. Our main purpose in this paper is to prove the global (in time) existence of solutions for the small data and their decay properties for the supercritical nonlinearities.
Databáze:	OpenAIRE
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