论文信息 - A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves

A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves

Modelling vertical nonsteady groundwater flow with dynamic capillary pressure leads to a nonlinear diffusion-convection equation extended with a nonlinear third order term with two space derivatives and one time derivative. We consider the special case in which the original equation is the Burgers' equation and the third order term is linear. We investigate stability of travelling wave solutions of the resulting pseudo-parabolic Burgers' equation, for which we first obtain well-posedness results.

Josephus Hulshof | Carlota M. Cuesta | C. M. Cuesta | J. Hulshof

[1] William G. Gray,et al. Thermodynamic basis of capillary pressure in porous media , 1993 .

[2] Alain Bourgeat,et al. Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects , 1998 .

[3] G. I. Barenblatt,et al. Mathematical model of the non equilibrium water oil displacement in porous strata , 1997 .

[4] E. Hopf. The partial differential equation ut + uux = μxx , 1950 .

[5] Michael I. Weinstein,et al. Oscillatory instability of traveling waves for a KdV-Burgers equation , 1993 .

[6] Josephus Hulshof,et al. Infiltration in porous media with dynamic capillary pressure: travelling waves , 2000, European Journal of Applied Mathematics.

[7] H. Brezis. Analyse fonctionnelle : théorie et applications , 1983 .

[8] G. I. Barenblatt,et al. Theory of Fluid Flows Through Natural Rocks , 1990 .

[9] A. Visintin. Differential models of hysteresis , 1994 .

[10] John R. King,et al. Analysis of a Darcy Flow Model with a Dynamic Pressure Saturation Relation , 1998, SIAM J. Appl. Math..

[11] R. Pego. Remarks on the stability of shock profiles for conservation laws with dissipation , 1985 .

[12] Michel Pierre,et al. On the Maximum Principle for Pseudoparabolic Equations. , 1980 .