Nonclassical Symmetries for a Class of Reaction-Diffusion Equations: the Method of Heir-Equations

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

Averaging principle for a class of stochastic reaction–diffusion equations

We consider the averaging principle for stochastic reaction–diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical ...

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

A numerical algorithm for solving a class of matrix equations

In this paper, we present a numerical algorithm for solving matrix equations $(A otimes B)X = F$  by extending the well-known Gaussian elimination for $Ax = b$. The proposed algorithm has a high computational efficiency. Two numerical examples are provided to show the effectiveness of the proposed algorithm.

Interior Controllability of a Broad Class of Reaction Diffusion Equations

We prove the interior approximate controllability of the following broad class of reaction diffusion equation in the Hilbert spaces Z L2 Ω given by z′ −Az 1ωu t , t ∈ 0, τ , where Ω is a domain in R, ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u ∈ L2 0, t1;L Ω and A : D A ⊂ Z → Z is an unbounded linear operator with the followi...