Related papers: Initial-boundary value problem for 2D micropolar e…
In this paper we study the solvability of different boundary value problems for the two dimensional steady incompressible Euler equation. Two main methods are currently available to study those problems, namely the Grad-Shafranov method and…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We consider initial boundary-value problems for nonlinear systems of conservation laws in one space variable. It is known that in general different viscous mechanisms yield different solutions in the zero-viscosity limit. Here we focus on…
We show local existence and uniqueness of plasma(fluid)-vaccum free boundary problem of magnetohydrodynamic flow in three-dimensional space with infinite depth setting when magnetic field is zero on the free boundary. We use…
This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The problem is considered in a bounded and connected domain $\Omega…
We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…
This paper is a follow-up of article [Gerard-Varet and Lacave, ARMA 2013], on the existence of global weak solutions to the two dimensional Euler equations in singular domains. In [Gerard-Varet and Lacave, ARMA 2013], we have established…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
The incompressible Micropolar system is given by two coupled equations: the first equation gives the evolution of the velocity field u while the second equation gives the evolution of the microrotation field $\omega$. In this article we…
We are concerned with an initial boundary value problem for the compressible magnetohydrodynamic equations with viscosity depending on the density. It is show that for the initial density away from vacuum, the strong solution to the problem…
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…
We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics.…
We prove that boundary value problems for fully nonlinear second-order parabolic equations admit $L_{p}$-viscosity solutions, which are in $C^{1+\alpha}$ for an $\alpha\in(0,1)$. The equations have a special structure that the "main" part…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting…
This paper is concerned with the initial-boundary value problem on the full Euler-Poisson system for ions over a half line. We establish the existence of stationary solutions under the Bohm criterion similar to the isentropic case and…
In this paper, we study the initial and boundary value problem of the Navier-Stokes equations in the half space. We prove the unique existence of weak solution $u\in L^q(\R_+\times (0,T))$ with $\nabla u\in L^{\frac{q}{2}}_{loc}(\R_+\times…
We consider 3D micropolar flows with possible vanishing spin viscosity and investigate the decay of the energy for large times. We compute first the exact $L^2$-asymptotic profile, as $t\to+\infty$, for solutions to the linear 3D micropolar…
In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…