Exponentially-bounded solutions of a system of parabolic equations

Abstract

In this article we study the existence of exponentially-bounded solutions of the following non-linear system of parabolic equations with homogeneous Neumann boundary conditions

where

is a diagonal matrix with

and Ω is a bounded domain in

. Under some conditions we prove the existence of a continuous manifold such that any solution with initial condition in this manifold is exponentially bounded.

Keywords:

• System of parabolic equations
• exponentially bounded solution
• AMS (MOS) Subject Classifications: Primary: 35B35
• Secondary: 35K57

Acknowledgments

Acosta's work was partially supported by CDCH-UCV and Leiva's work was partially supported by CDCHT-ULA.

Notes

E-mail [email protected]

Additional information

Notes on contributors

Hugo Leiva †

E-mail [email protected]