Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

Boundary Value Problems for Higher Order Parabolic Equations

We consider a constant coefficient parabolic equation of order 2m and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order m−1 lie in L2 with respect to surface measure. In addition, a regularity result for the solution is obtained if...

Initial - Boundary Value Problems for Parabolic Equations

The variational iteration method for a class of tenth-order boundary value differential equations

Boundary control for a class of pseudo-parabolic differential equations

The boundary stabilization problem for a class of linear and nonlinear pseudo-parabolic differential equations is considered. The proposed control laws are used to achieve global exponential stability for the linear system and semi-global exponential stability for the nonlinear system in the H 1-sense. An H 2 bound of the solution for the nonlinear system is also derived. A numerical example is...

Positive Solutions of a Nonlinear Higher Order Boundary-value Problem

The authors consider the higher order boundary-value problem u(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i−1)(0) = u(n−2)(p) = u(n−1)(1) = 0, 1 ≤ i ≤ n− 2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.