GLOBAL EXISTENCE, UNIQUENESS, AND STABILITY FOR A NONLINEAR HYPERBOLIC-PARABOLIC PROBLEM IN PULSE CO

A global existence theorem is established for an initial-boundary value problem,with time-dependent boundary data,arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonlinear mixed hyperbolic-parabolic system.Using results previously established for the associated linear problem,a fixed point argunent is employed to prove local existence for a regularized version of the nonlinear problem with artificial viscosity. Appropriate a-priori estimates are then derived which imply that the local existence result can be extended to a global existence theorem for the regularized problem.Finally,a different set of a priori estimates is generated which allows for taking the limit as the artificial viscosity parameter converges to zero; the corresponding solution of the regularized problem is then proven to converge to the unique solution of the initial-boundary value problem for the original,nonlinear,hyperbolic-parabolic system.