## Advances in Differential Equations

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

### Singular limit of some quasilinear wave equations with damping terms

#### 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