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Time Singular Limit of Semilinear Wave Equations with Damping

✍ Scribed by B. Najman

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
617 KB
Volume
174
Category
Article
ISSN
0022-247X

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✦ Synopsis

The hyperbolic semilinear initial value problem (\varepsilon u_{t}+A u_{1}+B u+f(u)=0), (u(0)=u_{0,}, u_{t}(0)=u_{1 s}), with commuting positive selfadjoint operators (A) and (B) in a Hilbert space (X) is considered. The term (A u), is a damping term. It is shown that the solutions converge, uniformly in time, in an appropriate Hilbert space 7 , to the solution of the parabolic type initial value problem (u_{t}+A{ }^{\prime} B u+A \quad f(u)=0), (u(0)=u_{00}) provided (u_{0}) converge to (u_{(0)}), and (u_{1 k}, f, A), and (B) satisfy certain conditions. The applications include different initial-boundary value problems from continuum mechanics. ' 1993 Academic Press. Ins

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