Initial boundary value problem for generalized Zakharov equations

Initial-Boundary Value Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

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...

Initial - Boundary Value Problems for Parabolic Equations