Branching of automorphic fundamental solutions

Almost Automorphic Solutions of Difference Equations

We study discrete almost automorphic functions sequences defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f n , we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Δu n Tu n f n . We also prove the existence of a discrete almost autom...

Fundamental Solutions of Dynamic Poroelasticity and Generalized Termoelasticity

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients

Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients

In this paper existence and asymptotic stability of asymptotically almost automorphic solution of impulsive neural networks with delay is discussed. The results are established by using various fixed point theorems and Lyapunov-like functional. As far as we know, this is the first paper to discuss such kind of solutions for impulsive neural networks. At the end, we give few examples to illustra...

Preconditioners and Fundamental Solutions

1. Introduction. The topic of this Licentiate thesis is the iterative solution of large, sparse systems of equations originating from discretizations of partial differential equations (PDEs). Our approach is to construct a preconditioner that is a truncated discrete convolution operator. The kernel is a fundamental solution, or an approximation of one. Our method generalizes to linear systems w...