Related papers: Well-posed two-point initial-boundary value proble…
A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial…
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…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zero and showing existence of solutions for the singular…
The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the…
We present a method to solve initial-boundary value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A. S. Fokas to solve initial-boundary…
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…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
We consider an initial value problem for time-fractional evolution equation in Banach space $X$: $$ \pppa (u(t)-a) = Au(t) + F(t), \quad 0<t<T. \eqno{(*)} $$ Here $u: (0,T) \rrrr X$ is an $X$-valued function defined in $(0,T)$, and $a \in…
In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric…
We establish local well-posedness for the higher-order nonlinear Schr\"odinger equation, formulated on the half-line. We consider the scenario of associated coefficients such that only one boundary condition is required, which is assumed to…
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 describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve…
This work studies the initial-boundary value problem of the two-dimensional nonlinear Schr\"odinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It…
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
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…
An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve $3 \times 3$ matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical…