## Differential and Integral Equations

- Differential Integral Equations
- Volume 8, Number 7 (1995), 1859-1866.

### Non-symmetric hyperbolic problems with different time scales

Heinz-Otto Kreiss, Fredrik Olsson, and Jacob Yström

#### Abstract

We study the Cauchy problem for nonsymmetric hyperbolic differential operators with different time-scales $P=\frac{1}{\epsilon} P_0(\frac{\partial}{\partial x}) + P_1(x,t,\frac{\partial}{\partial x}),$ $0<\epsilon \ll1$. Sufficient conditions for well-posedness independently of $\epsilon$ are derived. The bounded derivative principle is also shown to be valid, i.e., there exists smooth initial data such that a number of time derivatives are uniformly bounded initially. This gives an existence theory for the limiting equations when $\epsilon \rightarrow 0$. We apply our theory to the slightly compressible upper convected Maxwell model describing viscoelastic fluid flow.

#### Article information

**Source**

Differential Integral Equations, Volume 8, Number 7 (1995), 1859-1866.

**Dates**

First available in Project Euclid: 12 May 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1368397763

**Mathematical Reviews number (MathSciNet)**

MR1347986

**Zentralblatt MATH identifier**

0828.35011

**Subjects**

Primary: 35L25: Higher-order hyperbolic equations

Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 65M12: Stability and convergence of numerical methods 73F15 76A10: Viscoelastic fluids

#### Citation

Yström, Jacob; Olsson, Fredrik; Kreiss, Heinz-Otto. Non-symmetric hyperbolic problems with different time scales. Differential Integral Equations 8 (1995), no. 7, 1859--1866. https://projecteuclid.org/euclid.die/1368397763