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1995 Non-symmetric hyperbolic problems with different time scales
Heinz-Otto Kreiss, Fredrik Olsson, Jacob Yström
Differential Integral Equations 8(7): 1859-1866 (1995).

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.

Citation

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Heinz-Otto Kreiss. Fredrik Olsson. Jacob Yström. "Non-symmetric hyperbolic problems with different time scales." Differential Integral Equations 8 (7) 1859 - 1866, 1995.

Information

Published: 1995
First available in Project Euclid: 12 May 2013

zbMATH: 0828.35011
MathSciNet: MR1347986

Subjects:
Primary: 35L25
Secondary: 35B30, 65M12, 73F15, 76A10

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 7 • 1995
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