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August  2014, 19(6): 1627-1665. doi: 10.3934/dcdsb.2014.19.1627

The linear hyperbolic initial and boundary value problems in a domain with corners

 1 The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana 47405 2 The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Bloomington, Indiana 47405

Received  October 2013 Revised  March 2014 Published  June 2014

In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of Fourier analysis to achieve the well-posedness of the linear hyperbolic system, and we find by diagonalization that there are only two elementary modes in the system which we call hyperbolic and elliptic modes. The hyperbolic system in consideration is either symmetric or Friedrichs-symmetrizable.
Citation: Aimin Huang, Roger Temam. The linear hyperbolic initial and boundary value problems in a domain with corners. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1627-1665. doi: 10.3934/dcdsb.2014.19.1627
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