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Life-Span of solutions to nonlinear dissipative evolution equations: a singular perturbation approach
Milani, Albert
2000
Abstract
We investigate the large time behavior of solutions to nonlinear dissipative
wave equations of the general form
\[
\varepsilon u_{tt}+u_{t}-\Delta u=F\left(x,t,u,D_{x}u,D_{x}^{2}u\right);
\]
in particular, we study the dependence of the solutions $u=u^{\varepsilon}$
and of their life span $T_{\varepsilon}$ on the (small'' parameter
$\varepsilon$. We are interested in the behavior of $u^{\varepsilon}$
and $T_{\varepsilon}$ as $\varepsilon\rightarrow0$, and in their
relations with the solution v, and its life span T$_{p}$ , of the
corresponding limit equation when $\varepsilon=0$, which is of parabolic
type. We look for conditions under which either $T_{\varepsilon}=+\infty,\: or\: T_{\varepsilon}\rightarrow T_{p}\leq+\infty$
as $\varepsilon=0$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.2
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Albert Milani, "Life-Span of solutions to nonlinear dissipative evolution equations: a singular perturbation approach", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (2000) suppl.2, pp. 189-208.
Languages
en
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