Asymptotic Behaviour of the Eenergy to the Viscoelastic Wave Equation with Localized Hereditary Memory and Supercritical Source Term.

Autor:	Cavalcanti, V. N. Domingos, Cavalcanti, M. M., Marchiori, T. D., Webler, C. M.
Předmět:	POTENTIAL well HISTORICAL source material BLOWING up (Algebraic geometry)
Zdroj:	Journal of Dynamics & Differential Equations; Dec2023, Vol. 35 Issue 4, p3381-3431, 51p
Abstrakt:	We are concerned with the well-posedness of solutions as well as the asymptotic behaviour of the energy related to the viscoelastic wave equation with localized memory with past history and supercritical source and damping terms, posed on a bounded domain Ω ⊂ R 3 . Avoiding any relation between the damping and source terms, we obtain the global existence of solutions and the uniform energy decay rates, introducing the notion of a potential well and defining the expanded total energy functional. We also prove that weak solutions blow-up in finite time. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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