Advances in Differential Equations

Singular limit of some quasilinear wave equations with damping terms

Tokio Matsuyama

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Abstract

We consider a relation between a mixed problem for a class of quasilinear wave equations with small parameter $\epsilon$ and a reduced problem of a parabolic type. By constructing the stable set the global existence of solutions can be discussed. It is shown that the solution $u_{\epsilon}$ of the mixed problem converges, uniformly on any finite time interval, to the solution $u$ of the parabolic equation in an appropriate Hilbert space as $\epsilon \rightarrow 0$. Several $\epsilon$ weighted energy estimates will be obtained in order to evaluate the difference norm of $u_{\epsilon}-u$

Article information

Source
Adv. Differential Equations Volume 1, Number 2 (1996), 151-174.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896235

Mathematical Reviews number (MathSciNet)
MR1363999

Zentralblatt MATH identifier
0841.35012

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B25: Singular perturbations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]

Citation

Matsuyama, Tokio. Singular limit of some quasilinear wave equations with damping terms. Adv. Differential Equations 1 (1996), no. 2, 151--174. https://projecteuclid.org/euclid.ade/1366896235.


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