Related papers: Behavior of Solutions to An Initial Boundary Value…
Consider the planar restricted $(N+1)$-body problem with trajectories of the $N(\ge 2)$ primaries forming a collision-free periodic solution of the $N$-body problem, for any positive energy $h$ and directions $\theta_{\pm} \in [0, 2\pi)$,…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.
In bounded $n$-dimensonal domains with $n\ge 1$, this manuscript examines an initial-boundary value problem for the system \[ \left\{ \begin{array}{l} u_{tt} = \nabla \cdot (\gamma(\Theta) \nabla u_t) + a \nabla \cdot (\gamma(\Theta) \nabla…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
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…
We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…
This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn-Hilliard type; an additional convective term with a forced velocity field, which could act as a control on the…
Diffusion of a penetrating liquid in a polymeric material does not often satisfy the classical diffusion equations and requires taking relaxational (viscoelastic) properties of the polymer into account. We investigate a boundary value…
This paper is concerned with initial-boundary-value problems of general multi-dimensional hyperbolic relaxation systems with characteristic boundaries. For the characteristic case, we redefine a Generalized Kreiss condition (GKC) which is…
We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…
We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the one-dimensional compressible isentropic micropolar fluid model in a half line \mathbb{R}_{+}:=(0,\infty). We mainly investigates the…
In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some…