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In this paper the Liapunov functionals has been constructed, the decay property of the high dimensional modes of the J-J equations in the Josephson junctions is obtained, and thus the approximate inertial manifolds are given.

Abstract: A system of reaction-diffusion equations with two attractors is given in this paper. The construction of the attractors is discussed.

On the basis of an a priori estimate for solutions of a linear half-Dirichlet problem in the unit ball first order equations with the Di-rac operator as principal part for Clifford algebravalued functions an existence and uniqueness result is proved for a related nonlinear problemAn approximation procedure is used and an error estimate given.

This paper deals with boundary value problem for the first order qualilinear elliptic systems in the plane [image omitted] [image omitted]  where G is a unit disk with the boundary Г D is the Douglis' differential operator [image omitted]  Taking account of different signs for the problem's index n, first some a-priori estimates for the linear problem are given, then existence and uniqueness of the classical solution to the nonlinear problem are established under some hypotheses and well-posed conditions by a combination of an imbedding method with a Newton method.

In this paper the general solution of the equation (D - λ)w = 0 in SO(m)-invariant open subsets όmega of Rm is obtained, whereby D is the Dirac operator and λ is a complex constant. The results thus obtained are used to solve the eigenvalue problem for the Dirac operator corresponding to the half-Dirichlet problem for the unit ball in Rm and to construct the fundamental solution of D - λ and integral representation formulae.