On Multicomponent Fluid Mixtures
نویسنده
چکیده
We consider the flow of the mixture of viscous, heat-conducting, compressible fluids consisting of n different components, each of which has its own density, pressure, and molecular weight but all components having the same velocity and temperature. The mathematical model presented here relies on fundamental principles of continuum mechanics and combustion, where the balance laws, the constitutive relations, and other assumptions on the model are based on the following considerations. (a) We treat the material (gas) as a viscous, compressible, heat-conducting fluid, occupying a bounded domain Ω in the physical space R3, which is a perfect mixture of n species of real monoatomic gases Fermi gases. (b) The motion of the gas is an entropy producing (dissipative) process. The transport fluxes satisfy very general constitutive laws taking into account the multicomponent character of the mixture. The reaction rate satisfies a general Arrhenius-type law and the transport coefficients depend on the absolute temperature. (c) The pressure depends on the volume fractions of the individual species; it takes into consideration both the chemical reaction of the individual component as well as radiation effects. The aim of this work is to establish the global existence and weak asymptotic stability of solutions to the initial boundary value problem with large initial data. This work extends earlier works on the study of the dynamics of mixtures of compressible fluids [37], [38] (see also [15], [16]) since it now treats a physically relevant multidimensional, multicomponent combustion model which complies with the fundamental principles of continuum mechanics
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تاریخ انتشار 2006