Related papers: Complex Ginzburg-Landau equations with dynamic bou…
In this paper well-posedness is proved for an initial and boundary value problem (IBVP) relative to a large class of quasilinear hyperbolic systems, in $p+q$ equations, on a strip, arising from a model of $H_2O$-phase transitions in the…
We study the local in time well-posedness of the initial boundary value problem (IBVP) for the vacuum Einstein equations in general relativity with geometric boundary conditions. For conformal-mean curvature boundary conditions, consisting…
We prove local well-posedness for the initial-boundary value problem (IBVP) associated to the Schr\"odinger-Korteweg de Vries system on right and left half-lines. The results are obtained in the low regularity setting by using two analytic…
We study an initial-boundary-value problem (IBVP) for a system of coupled Maxwell-Bloch equations (CMBE) that model two colors or polarizations of light resonantly interacting with a degenerate, two-level, active optical medium with an…
The complex Ginzburg Landau equation (CGLE) is a ubiquitous model for the evolution of slowly varying wave packets in nonlinear dissipative media. A front (shock) is a transient layer between a plane-wave state and a zero background. We…
We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations by describing the boundary conditions of a spacetime metric in its associated gauge. This gauge is determined, equivariantly with respect to…
We consider initial-boundary value problems (IBVPs) on a finite interval for the system of the energy balance equation and Guyer-Krumhansl constitutive equation. Boundary conditions comprise various models of behavior of a physical system…
In this work, we consider the initial value problem (IVP) for a system of modified Korteweg-de Vries (mKdV) equations \begin{equation} \begin{cases} \partial_t v + \partial_x^3 v+ \partial_x (v w^2) = 0, \hspace{0.98 cm} v(x,0)=\psi(x),\\…
We aim to prove a unique solvability of an initial-boundary value problem (IBVP) for a time-fractional wave equation in a rectangular domain. We exploit the spectral expansion method as the main tool and used the solution to Cauchy problems…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
The initial-boundary value problem for the inhomogeneous non-cutoff Boltzmann equation is a challenging open problem. In this paper, we study the stability and long-time dynamics of the Boltzmann equation near a global Maxwellian without…
The purpose of the present research is to investigate model mixed boundary value problems for the Helmholtz equation in a planar angular domain $\Omega_\alpha\subset\mathbb{R}^2$ of magnitude $\alpha$. The BVP is considered in a…
Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…
The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the inhomogeneous nonlinear Schr\"odinger equation (INLS) $$ i u_t +\Delta u+\lambda|x|^{-b}|u|^\alpha u = 0, $$ where $\lambda=\pm 1$ and $\alpha$,…
We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…
In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of…
This paper is a continuation of authors' previous work \cite{CK2018-1}. We extend the argument \cite{CK2018-1} to fifth-order KdV-type equations with different nonlinearities, in specific, where the scaling argument does not hold. We…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the…