Automatic Symmetrization and Energy Estimates Using Local Operators for Partial Differential Equations |
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Authors: | Thomas Hagstrom Daniel Appelö |
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Affiliation: | 1. Department of Mathematics and Statistics , The University of New Mexico , Albuquerque, New Mexico, USA hagstrom@math.unm.edu;3. Department of Numerical Analysis and Computer Science , Royal Institute of Technology , Stockholm, Sweden |
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Abstract: | We develop a method for automatically symmetrizing Petrowsky well-posed Cauchy problems for constant coefficient linear partial differential equations. The method is rooted in the Sturm sequence technique for establishing the location of the roots of a complex polynomial and can be automated using standard symbolic computation tools. In the special case of homogeneous strictly hyperbolic scalar equations, we show that the resulting estimates are strong enough to control all principal order derivatives and thus can be used in place of the Leray energies. We also illustrate the method by applying it to various problems of mixed type. |
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Keywords: | Cauchy problem Energy estimates Sturm sequences Well-posedness |
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