New methods for local solvability of quasilinear symmetric hyperbolic systems

MohanManil T.; Sivaguru S.  Sritharan

doi:10.3934/eect.2016005

Article Contents

2016, Volume 5, Issue 2: 273-302. Doi: 10.3934/eect.2016005

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New methods for local solvability of quasilinear symmetric hyperbolic systems

MohanManil T.^1, and
Sivaguru S. Sritharan^2,

1.
Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, OH 45433
2.
Office of the Provost & Vice Chancellor, Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, OH 45433

Received: December 31, 2015

Revised: April 30, 2016

Published: May 2016

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Abstract

In this work we establish the local solvability of quasilinearsymmetric hyperbolic system using local monotonicity method andfrequency truncation method. The existence of an optimal control isalso proved as an application of these methods.

Keywords:

Quasilinear symmetric hyperbolic equations,
commutator estimates,
local monotonicity,
Minty-Browder,
optimal control.

Mathematics Subject Classification: Primary: 35L60; Secondary: 35L90, 35L45, 49J20.

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