Acta mathematica scientia, Series B >
GLOBAL EXISTENCE, UNIQUENESS, AND STABILITY FOR A NONLINEAR HYPERBOLIC-PARABOLIC PROBLEM IN PULSE COMBUSTION
Received date: 2011-07-12
Online published: 2012-01-20
Supported by
The research reported in this paper is based, in large measure, on the Ph.D. dissertation of the first author at Northern Illinois University.
A global existence theorem is established for an initial-boundary value prob-lem, 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 sys-tem. Using results previously established for the associated linear problem, a fixed point argument 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 di?erent set of a priori estimates is generated which allows for takingthelimit as theartificial viscosity parameter converges tozero; 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.
Olga Terlyga , Hamid Bellout , Frederick Bloom . GLOBAL EXISTENCE, UNIQUENESS, AND STABILITY FOR A NONLINEAR HYPERBOLIC-PARABOLIC PROBLEM IN PULSE COMBUSTION[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 41 -74 . DOI: 10.1016/S0252-9602(12)60004-6
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