Related papers: Complex Ginzburg-Landau equations with dynamic bou…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded…
We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on the right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic…
This paper concerns the initial-boundary value problem (IBVP) of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing…
In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…
This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the…
We consider the initial value problem (IVP) associated to a quadratic Schr\"odinger system \begin{equation*} \begin{cases} i \partial_{t} v \pm \Delta_{g} v - v = \epsilon_{1} u \bar{v}, & t \in \mathbb{R},\; x \in M, \\[2ex] i \sigma…
We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of {\em arbitrary order}, posed on the domain $\{t>0, 0<x<L\}$. We first show that by analysing…
In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…
A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is…
In this paper, the initial boundary value problem of the Korteweg-de Vries Burger equation on the negative half-plane is analyzed. Initially, the well-posedness on $H^s(\R^-)$ for $s\geq 0$ of the IBVP is established to concentrate on the…
This paper deals with controllability properties of a cubic Ginzburg-Landau equation with dynamic boundary conditions. More precisely, we prove a local null controllability result by using a single control supported in a small subset of the…
We investigate the mixed Dirichlet-Neumann boundary value problems for the Laplace-Beltrami equation on a smooth hypersurface $\mathcal{C}$ with the smooth boundary in non-classical setting in the Bessel potential spaces…
In this paper, the well-posedness is studied for the initial boundary value problem of the two-dimensional compressible ideal magnetohydrodynamic (MHD) equations in bounded perfectly conducting domains with corners. The presence of corners…
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…
We consider a boundary value problem of a stationary advection equation in a bounded domain with Lipschitz boundary. It is known to be well-posed in $L^p$-based function spaces for $1 < p < \infty$ under the separation condition of the…
The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular grid that is independent of the geometry, the IB framework…
In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility…
A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion-reaction problem with a reaction parameter tending…
We consider the stability of front-type modulated waves in the complex Ginzburg-Landau equation (CGL). The waves occur in the bistable regime (e.g. of the quintic CGL) and connect the zero state to a spatially homogenous state oscillating…