A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions

In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g , the function Φ, p > max { ρ + 2 , m , q , 2 } , and the initial data, we prove a global nonexistence of solutions for a quasiline...

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Veröffentlicht in:	Boundary value problems 2018-09, Vol.2018 (1), p.1-19, Article 139
Hauptverfasser:	Kang, Yong Han, Park, Jong Yeoul, Kim, Daewook
Format:	Artikel
Sprache:	eng
Schlagworte:	Acoustic boundary conditions Analysis Approximations and Expansions Blow-up of solution Boundary conditions Difference and Functional Equations Global nonexistence of solution Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Quasilinear viscoelastic wave equation Viscoelasticity Wave equations
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Zusammenfassung:	In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g , the function Φ, p > max { ρ + 2 , m , q , 2 } , and the initial data, we prove a global nonexistence of solutions for a quasilinear viscoelastic wave equation with positive initial energy.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-018-1057-0