Related papers: Integrable initial boundary value problems
The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary…
Initial-boundary value problems on a half-strip with different types of boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov equation with nonlinearity of higher order are considered. In particular, nonlinearity can be…
We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…
The initial boundary value problems for compressible Navier-Stokes-Poisson is considered on a bounded domain in $\mathbb{R}^3$ in this paper. The global existence of smooth solutions near a given steady state for compressible…
We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general…
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…
In this paper we analyse some possibilities of finding positive solutions for second order boundary value problems with Dirichlet and periodic boundary conditions, for which the correspondent Green's functions change sign. The obtained…
In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-in-time existence of classical solution to the initial-boundary value problem by the method of energy…
In this paper we present some open problems pertaining to the approximation theory involved in the solution of the important class of Nonlinear Partial Differential Equations (NPDEs) of integrable type. For this class of NPDEs, any Initial…
We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.
In this work we prove that the initial-boundary value problem (IBVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_t+\partial_x^5 u+u\partial_x u&\hspace{-2mm}=0,&\quad x\in\mathbb R^+,\;…
Two-point boundary value problems for a discrete Ermakov-Painlev\'e II equation are analysed by means of topological methods. In addition, an alternative variational approach is detailed. Existence of solutions is established for…
In this paper, by using the Krasnosel'skii's fixed-point theorem, we study the existence of at least one or two positive solutions to the three-point integral boundary value problem {equation*} \label{eq-1} {gathered} {u^{\prime…
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is…
We classify integrable third order equations in 2+1 dimensions which generalize the examples of Kadomtsev-Petviashvili, Veselov-Novikov and Harry Dym equations. Our approach is based on the observation that dispersionless limits of…
We study the boundary value problem with Radon measures for nonnegative solutions of $-\Delta u+Vu=0$ in a bounded smooth domain $\Gw$, when $V$ is a locally bounded nonnegative function. Introducing some specific capacity, we give…
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the…
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…