Electron. J. Diff. Equ., Vol. 2013 (2013), No. 46, pp. 1-42.

A hyperbolic-parabolic system arising in pulse combustion: existence of solutions for the linearized problem

Olga Terlyga, Hamid Bellout, Frederick Bloom

Abstract:
A mixed hyperbolic-parabolic system is derived for a lumped parameter continuum model of pulse combustion. For a regularized version of the initial-boundary value problem for an associated linear system, with time-dependent boundary conditions, Galerkin approximations are used to establish the existence of a suitable class of unique solutions. Standard parabolic theory is then employed to established higher regularity for the solutions of the regularized problem. Finally, a priori estimates are derived which allow for letting the artificial viscosity, in the regularized system, approach zero so as to obtain the existence of a unique solution for the original mixed hyperbolic-parabolic problem.

Submitted July 10, 2012. Published February 8, 2013.
Math Subject Classifications: 35M33, 35B65, 80A25.
Key Words: Pulse combustion; linear hyperbolic-parabolic system; Galerkin approximation; global solution.

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  Olga Terlyga
Fermi National Laboratory
Batavia, IL 60510, USA
email: terlyga@fnal.gov
Hamid Bellout
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60115, USA
email: sabachir@hotmail.com
Frederick Bloom
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60115, USA
email: bloom@math.niu.edu, Phone 815-753-6765

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