An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed. To construct approximation in time, regularized twolevel schemes are used. The numerical implementation is based on solving the equation with the square root...

In this paper, a new pseudoparabolic equation with logarithmic nonlinearity of variable exponents is investigated. By using the energy functional and classical potential well, we obtain global existence blow-up results weak solutions exponents. These extend improve some recent in which were showed involving

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stabl...

and Applied Analysis 3 where α > 0, λ > 0, and p > 1. Their proof revealed that if the initial data is small enough, then there exists a unique solution. Once removing the assumption that the initial data is small, then one should addN ≤ 4 with p > 1 orN ≥ 5 with 1 < p ≤ N/ N−4 to assure the existence of a unique solution. Further, from their results, one can also find that the solutions of 1.5...

In this paper, we consider the Robin-Dirichlet problem for a system of nonlinear pseudoparabolic equations with viscoelastic term. By Faedo-Galerkin method, first prove existence and uniqueness solution problem. Next, give sufficient condition to get global decay weak solution. Finally, by concavity blow-up result when initial energy is negative. Furthermore, establish here lifespan finding upp...

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota&apos;s bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...