Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T , there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T . In addition, the global convergence and regularity of series solutions is established for initial data satisfying mil...

In this article, we study the existence and asymptotic stability in pth moment of mild solutions to second order neutral stochastic partial differential equations with delay. Our method of investigating the stability of solutions is based on fixed point theorem and Lipchitz conditions being imposed.

Existence of mild solutions for the 3D MHD system in bounded Lipschitz domains is established critical spaces with absolute boundary conditions.

We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces.We use Fan-KKM lemma and concept of η-cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalit...

We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the nonlinearity prevents us from showing the uniqueness of the solutions as well as their boundedness (in time).

In this paper the authors study the existence and asymptotic stability in p-th moment of mild solutions to stochastic neutral partial differential equation with impulses. Their method for investigating the stability of solutions is based on the fixed point theorem.

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Naiver-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of Q α, loc (R). This result applies to the usual incompressible Navier-Stokes equations and deduces a known link.

We consider static spherically symmetric solutions of the Einstein equations with cosmological constant Λ coupled to the SU(2) Yang Mills equations. We prove that under relatively mild conditions, any solution can be continued back to the origin of spherical symmetry and that the qualitative behavior of the solutions near the origin does not depend on Λ.

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. c © 2006 Elsevier Ltd. All rights reserved.

We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the nonlinearity prevents us from showing the uniqueness of the solutions as well as their boundedness (in time).