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 | |
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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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