In this paper we look for solutions of the equation δdA = f (〈A,A〉)A in R, where A is a 1-differential form and k ≥ 2. These solutions are critical points of a functional which is strongly degenerate because of the presence of the differential operator δd. We prove that, assuming a suitable convexity condition on the nonlinearity, the equation possesses infinitely many finite energy solutions.

We consider the nonlinear damped wave equation arising in unsteady Poiseuille flow of shear thinning Maxwell fluid. We show the global existence of the smooth solution to the corresponding nonlinear system. We also give some numerical examples. c © 2006 Elsevier Ltd. All rights reserved.

The time-dependent Maxwell system is supplemented with the constitutive relations of linear bianisotropic media and is treated as a neutral integro-differential equation in a Hilbert space. By using the theory of abstract Volterra equations and strongly continuous semigroups we obtain general well-posedness results for the corresponding mathematical problem.

This paper deals with an identification problem for degenerate parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Existence, uniqueness and continuous dependence results are proved for the problem. Applications to the source identification problems for the Poissonheat e...

We develop a formalism for efficient iterative solutions of scattering problems involving the Maxwell equations. The methods, borrowed from recent advancements in chemical reaction dynamics, represent the scattering wavefunctions on two grids; one used for the initial wave and is one-dimensional; the other is a small three-dimensional grid padded with absorbing-potentials on which the scattered...

Time local well-posedness for the Maxwell-Schrödinger equation in the Coulomb gauge is studied in Sobolev spaces by the contraction mapping principle. The Lorentz gauge and the temporal gauge cases are also treated by the gauge transform. Mathematics Subject Classification (2000) : 35Q55, 35Q60, 35L70.

We prove that the critical Maxwell-Klein Gordon equation on R is globally well-posed for smooth initial data which are small in the energy. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.

Similarity reductions of the coupled nonlinear Schrödinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painlevé transcendents, leading to new exact self-similar solutions for these integrable equations. PACS numbers: 02.30.Ik., 02...