Analysis of model equations for stress-enhanced diffusion in coal layers. Part I: existence of a weak solution
- University of Lyon, Lyon (France)
This paper is motivated by the study of the sorption processes in the coal. They are modeled by a nonlinear degenerate pseudoparabolic equation for stress-enhanced diffusion of carbon dioxide (CO{sub 2}) in coal. These types of equations arise in a number of cases when nonequilibrium thermodynamics or extended nonequilibrium thermodynamics is used to compute the flux. For the given equation, existence of the travelling wave-type solutions was extensively studied. Nevertheless, the existence seems to be known only for a sufficiently short time. We use the corresponding entropy functional in order to get existence, for any time interval, of an appropriate weak solution with square integrable first derivatives and satisfying uniform L-infinity-bounds. Due to the degeneracy, we obtain square integrability of the mixed second order derivative only in the region where the concentration phi is strictly positive. In obtaining the existence result it was crucial to have the regularized entropy as unknown for the approximate problem and not the original unknown (the concentration).
- OSTI ID:
- 21150666
- Journal Information:
- Siam Journal on Mathematical Analysis, Vol. 40, Issue 4; ISSN 0036-1410
- Country of Publication:
- United States
- Language:
- English
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