Differential and Integral Equations

Non-symmetric hyperbolic problems with different time scales

Heinz-Otto Kreiss, Fredrik Olsson, and Jacob Yström

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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


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