Theory of damped wave models with integrable and decaying in time speed of propagation

Autor(es)

Ebert, Marcelo Rempel ; Reissig, Michael

• Tipo de documento: Artigo Científico
• Fonte: Journal of Hyperbolic Differential Equations; v. 13, n. 2, p. 417-439, JUN 2016.
• Citações Web of Science: 6

Resumo

We study the Cauchy problem for damped wave equations with a timedependent propagation speed and dissipation. The model of interest is u(tt) - a(t)(2) Delta u + b(t)u(t) = 0, u(0, x) = u(0)(x), u(t)(0, x) = u(1)(x). We assume a is an element of L-1(R+). Then we propose a classification of dissipation terms in noneffective and effective. In each case we derive estimates for kinetic and elastic type energies by developing a suitable WKB analysis. Moreover, we show optimality of results by the aid of scale-invariant models. Finally, we explain by an example that in some estimates a loss of regularity appears. (AU)

• Processo FAPESP: 13/20297-8 - Estimativas do tipo L^p-L^q para equações diferenciais parciais hiperbólicas
• Beneficiário: Marcelo Rempel Ebert
• Linha de fomento: Bolsas no Exterior - Pesquisa