Exact controllability of the nonlinear third-order dispersion equation

Controllability of Nonlinear Third-order Dispersion Inclusions with Infinite Delay

This article shows the controllability of nonlinear third-order dispersion inclusions with infinite delay. Sufficient conditions are obtained by using a fixed-point theorem for multivalued maps. Particularly, the compactness of the operator semigroups is not assumed in this article.

On the Exact Controllability of a Nonlinear Stochastic Heat Equation

The bounded open subsetG of Rn is assumed to have a smooth boundary and g is continuous from L2(0,T ;L2(G)) into L2(0,T ;L2(G)). The existence of a solution of the linear version of (1.1) is established in Section 3 of the paper. The nonlinear case is considered in Section 4. The main assumptions of the paper and some preliminary results are given in Section 2. Exact controllability of the wave...

Exact Controllability for a Nonlinear Stochastic Wave Equation

Exact controllability of the superlinear heat equation

In this paper, we consider the controllability of a semilinear heat equation with a nonlinearity that has a superlinear growth at infinity with Dirichlet boundary conditions in a bounded domain of RN . The proof of the main result in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments.

Exact First-order Solutions of the Nonlinear Schrodinger Equation

A method is proposed for finding exact solutions of the nonlinear Schr~dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schr~dinger e...