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January/February 2009 On linear hyperbolic boundary-value problems
Rita Cavazzoni
Differential Integral Equations 22(1/2): 125-134 (January/February 2009).

Abstract

The paper deals with the well posedness of linear hyperbolic second-order systems with homogeneous boundary conditions, in the half-space $\Omega = {\bf R}^{d-1} \times (0,\infty)$. At first we consider operators with constant coefficients: by performing a Fourier-Laplace transform and by studying the space of the solutions, we prove a sufficient condition for the well posedness of the boundary-value problem, by means of the Hille-Yosida theorem. Subsequently, we study the case of evolution boundary-value problems for second-order systems with coefficients that depend on the space variable. Proving that the linear second-order operator associated with the system, under suitable assumptions, turns out to be maximal and monotone, we establish the well posedness of the problem by applying the Hille-Yosida theorem.

Citation

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Rita Cavazzoni. "On linear hyperbolic boundary-value problems." Differential Integral Equations 22 (1/2) 125 - 134, January/February 2009.

Information

Published: January/February 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35341
MathSciNet: MR2483015

Subjects:
Primary: 35L55

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 1/2 • January/February 2009
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