Related papers: Initial boundary value problem for Korteweg-de Vri…
In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.
We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
We construct solutions to the Schwarz boundary value problem on the unit disk and the upper half-plane when the boundary condition is with respect to boundary values in the sense of distributions.
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
In this work, we consider a number of boundary-value problems for time-fractional heat equation with the recently introduced Caputo-Fabrizio derivative. Using the method of separation of variables, we prove a unique solvability of the…
We consider the initial value problema (IVP) for the generalized Korteweg-de Vries (gKdV) equation \begin{equation} \begin{cases} \partial_tu+\partial_x^3u+\mu u^k\partial_xu=0, \,\;\; x\in \mathbb{R}, \, t \in \mathbb{R},\\ u(x,0)=u_0(x),…
Backward stochastic partial differential equations in bounded and unbounded domains are studied. Existence and regularity results are obtained. Duality relationship with forward SPDEs are established. Representation of functionals of Ito…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of…
For $\nu,\nu_i,\mu_j\in(0,1)$, we analyze the semilinear integro-differential equation on the one-dimensional domain $\Omega=(a,b)$ in the unknown $u=u(x,t)$ \[…
We consider the numerical computation of finite-genus solutions of the Korteweg-de Vries equation when the genus is large. Our method applies both to the initial-value problem when spectral data can be computed and to dressing scenarios…
This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…
This book considers posing and the methods of solving simple linear boundary-value problems in classical mathematical physics. The questions encompassed include: the fundamentals of calculus of variations; one-dimensional boundary-value…
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…
We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…
We investigate the influence of uncertain data on solutions to initial boundary value problems. Uncertainty in the forcing function, initial conditions and boundary conditions are considered and we quantify their relative influence for…