Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 46, pp. 1-42.

Title: A hyperbolic-parabolic system arising in pulse combustion:
       existence of solutions for the linearized problem
        
Authors: Olga Terlyga (Fermi National Laboratory, Batavia, IL, USA)
         Hamid Bellout   (Northern Illinois Univ., DeKalb, IL, USA)
         Frederick Bloom (Northern Illinois Univ., DeKalb, IL, USA)

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 08, 2013.
Math Subject Classifications: 35M33, 35B65, 80A25.
Key Words: Pulse combustion; linear hyperbolic-parabolic system;
           Galerkin approximation; global solution.