Initial Boundary Value Problem for the System of Compressible Adiabatic Flow Through Porous Media

Boundary Effects and Large Time Behavior for the System of Compressible Adiabatic Flow through Porous Media

On the Diffusive Profiles for the System of Compressible Adiabatic Flow through Porous Media

We study the Cauchy problem for the system of one dimensional compressible adiabatic flow through porous media and the related diffusive problem. We introduce a new approach which combines the usual energy methods with special L1-estimates and use the weighted Sobolev norms to prove the global existence and large time behavior for the solutions of the problems. The asymptotic states for the sol...

Initial Boundary Value Problem for Compressible Euler Equations with Relaxation

In this paper, we study the global exisitence of L∞ weak entropy solution to the initial boundary value problem for compressible Euler equations with relaxtion and the large time asymptotic behavior of the solution. Motivated by the sub-characterisitic conditions, we proposed some structural conditions on the relaxation term comparing with the pressure function. These conditions are proved to b...

Initial Boundary Value Problem For Compressible Euler Equations With Damping

We construct global L∞ entropy weak solutions to the initial boundary value problem for the damped compressible Euler equations on bounded domain with physical boundaries. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy’s law. Based on entropy principle, we showed that the physical weak solutions converges to st...

The Initial–boundary Riemann Problem for the Solution of the Compressible Gas Flow

The paper deals with a special way of the construction of boundary conditions for the compressible gas flow. The solution of the Riemann problem is used at the boundary. It can be shown, that the unknown one-side initial condition for this problem can be partially replaced by the suitable complementary condition. Authors work with such initial-boundary problem and suggest the complementary cond...