Related papers: Boundary Value Problems For Integrable Equations C…
In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval \begin{equation} u_t+u_x+u_{xxx}+uu_x=0,\qquad u(x,0)=\phi(x), \qquad 0<x<L, \ t>0 \qquad (1) \end{equation} subject…
We discuss relations between the initial boundary value problem (IBVP) and quasi-local Hamiltonians in GR. The latter have traditionally been based on Dirichlet boundary conditions, which however are shown here to be ill-posed for the IBVP.…
We discuss the $\zeta-$regularized determinant of elliptic boundary value problems on a line segment. Our framework is applicable for separated and non-separated boundary conditions.
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow…
Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
We review the theory of one-sided coupled operator matrices with a focus on evolution equations with inhomogeneous boundary conditions. (The original article had no abstract.)
This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial…
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…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
In the present work we investigate a boundary problem with non-local conditions, connecting values of seeking function on various characteristics for parabolic-hyperbolic equation with three lines of type changing. The considered problem is…
We consider a boundary-value problem for the second order elliptic differential operator with rapidly oscillating coefficients in a domain $\Omega_{\epsilon}$ that is $\epsilon-$periodically perforated by small holes. The holes are divided…
We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear elliptic partial differential equations. In particular, our…
Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of…
In this paper, a boundary-value problem for the 3-D wave equation with Caputo and Bessel operators is investigated. Sufficient conditions on the initial data are established for the existence of a unique solution to the considered problem.