Stabilizability of integro-differential parabolic equations

Linear Complexity Solution of Parabolic Integro-differential Equations

The numerical solution of parabolic problems ut + Au = 0 with a pseudodifferential operator A by wavelet discretization in space and hp discontinuous Galerkin time stepping is analyzed. It is proved that an approximation for u(T ) can be obtained in N points with accuracy O(N) for any integer p ≥ 1 in work and memory which grows logarithmically-linear in N .

Regularity estimates for parabolic integro- differential equations and applications

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...

The Generalized Quasilinearization Method for Parabolic Integro-differential Equations

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

Stabilizability of Bibo Integro-differential Systems with Two Distributed Delays

Control laws' design strategies are developed to stabilize a class of BIBO integro-differential systems with two distributed delays by using an extended system.

Nonlinear Integro - Differential Equations