Name
Title | ||
|---|---|---|
Analysis of Model Equations for Stress-Enhanced Diffusion in Coal Layers. Part I: Existence of a Weak Solution |
Abstract | ||
|---|---|---|
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(2)) in coal, partial derivative(t)phi = partial derivative(x) {D(phi) partial derivative(x)phi+D(phi)phi/B partial derivative(x) (e(-m phi)partial derivative(t)phi)}, where B, m are positive constants and the diffusion coefficient D(phi) has a small value when the CO(2) volume fraction phi is 0 <= phi < phi(c), representative of coal in the glass state and orders of magnitude higher value for phi > phi(c), when coal is in the rubber-like state. These types of equations arise in a number of cases when nonequilibrium thermodynamics or extended nonequilibrium thermodynamics is used to compute the flux. For this 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). |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1137/070710172 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
degenerate pseudoparabolic equation,entropy methods,stress-enhanced diffusion | Degenerate energy levels,Traveling wave,Second derivative,Mathematical analysis,Weak solution,Non linear model,Diffusion equation,Mathematics,Non-equilibrium thermodynamics | Journal |
Volume | Issue | ISSN |
40 | 4 | 0036-1410 |
Citations | PageRank | References |
1 | 0.72 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andro Mikelic | 1 | 109 | 21.66 |
| Hans Bruining | 2 | 1 | 0.72 |