in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

In this paper we prove a unique continuation result for a cascade system of parabolic equations, in which the solution of the first equation is (partially) used as a forcing term for the second equation. As a consequence we prove the existence of ε-insensitizing controls for some parabolic equations when the control region and the observability region do not intersect. Mathematics Subject Class...

The bidomain equations represent the most complete description of cardiac electrical activity. However, the equations prove computationally burdensome as the resulting system of equations has two entries per spatial node. This paper examines the computational performance obtained by decoupling the bidomain equations into two separate systems of equations, an elliptic equation for the extracellu...

We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the last two centuries. It was followed by the theory of parabolic equations of different types. In a parallel development, the theory of stochastic differential e...

CONTENTS Introduction 151 § 1. Maximal attractors of semigroups generated by evolution equations 156 § 2. Examples of parabolic equations and systems having a maximal attractor 158 § 3. The Hausdorff dimension of invariant sets 164 § 4. Estimate of the change in volume under the action of shift operators generated by linear evolution equations 167 § 5. An upper bound for the Hausdorff dimension...

Ageneral solution,basedontheseparationofvariablesmethod,for the thermal spreadingresistance incompound annular sectors, is presented. Results are given for three heat  ux distributions: inverse parabolic, uniform, and parabolic proŽ les. The general solution can be used to model any number of equally spaced heat sources on a compound or isotropic annulus. Graphical results are presented for a ...

We study the asymptotic behavior of Lipschitz continuous solutions of nonlinear degenerate parabolic equations in the periodic setting. Our results apply to a large class of Hamilton-Jacobi-Bellman equations. Defining Σ as the set where the diffusion vanishes, i.e., where the equation is totally degenerate, we obtain the convergence when the equation is uniformly parabolic outside Σ and, on Σ, ...

The objective of this work is to numerically determine the thermal performance parabolic cylinder cooker commonly “blazing tube”. These performances were determined by establishing heat balances at different levels system. equations obtained have been discretized; simplifying assumptions made facilitate their resolution. We adopted Gauss Seidel’s method using MATLAB software solve these equatio...

We address the self-similar solvability of a singular parabolic problem and show that solutions to parabolic fully nonlinear equations are not expected to be C.

Mohammed Kbiri Alaoui Department of Mathematics, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia Correspondence should be addressed to Mohammed Kbiri Alaoui, mka [email protected] Received 31 March 2011; Accepted 28 July 2011 Academic Editor: Mihai Putinar Copyright q 2011 Mohammed Kbiri Alaoui. This is an open access article distributed under the Creative Commons Attribution License, which...