Initial boundary value problems for the Carleman equation

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Initial-Boundary Value Problems for the Korteweg-de Vries Equation

Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and nonsteady solutions are possible. The an...

approximating initial-value problems with two-point boundary-value problems: bbm-equation

Approximating Initial-value Problems with Two-point Boundary-value Problems: Bbm-equation

The focus of the present study is the BBM equation which models unidirectional propagation of small amplitude, long waves in dispersive media. This evolution equation has been used in both laboratory and field studies of water waves. The principal new result is an exact theory of convergence of the two-point boundary-value problem to the initial-value problem posed on an infinite stretch of the...

Initial - Boundary Value Problems for Parabolic Equations