Correct initial boundary value problems for dispersive equations

Initial - Boundary Value Problems for Parabolic Equations

Non homogeneous boundary value problems for linear dispersive equations

While the non-homogeneous boundary value problem for elliptic, hyperbolic and parabolic equations is relatively well understood, there are still few results for general dispersive equations. We define here a convenient class of equations comprising the Schrödinger equation, the Airy equation and linear ‘Boussinesq type’ systems, which is in some sense a generalization of strictly hyperbolic equ...

Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations

It is suggested here that an interesting and important line of inquiry is the elaboration of methods of inverse scattering transform (IST) type in contexts where non-homogeneous boundary conditions intercede. The issue, which has practical relevance we indicate by example, appears ripe for development, thanks to recent new ideas interjected into the panoply of IST methodologies. A sketch of the...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

Initial Boundary Value Problems for Hyperbolic Partial Differential Equations

1, Differential equations in one space dimension. The simplest hyperbolic differential equation is given by (1.1) du/dt = cdu/dx, where c is a constant, Its general solution is u(x, t) — F(x + ci), i.e., it is constant along the "characteristic lines" x + ct = const (see Figure 1). Therefore, if we u(l,t) = g(t) u(0,t)*g(t want to determine the solution of (1.1) in the region 0 ^ x ^ 1, t ja 0,...