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Equivalence of Two Stabilization Schemes for a Class of Linear Parabolic Boundary Control Systems

Nambu T.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 2

187--199

The paper studies the stabilization problem for a class of linear parabolic boundary control systems with a Riesz basis. The author earlier proposed two different feedback control schemes to cope with the difficulties arising from the feedback terms on the boundary; these schemes are based on different ideas, and look fairly different from each other. We show, however, that they are algebraically similar.

Global solution to the initial value problem for nonlinear system of equations of thermodiffusion without displacements

Łazuka J.

Demonstratio Mathematica

2004

Vol. 37, nr 3

557--570

In the paper we shall present the proof of global-in-time solution to the initial value problem for nonlinear partial differential equations describing physical proc-cesses of thermodiffusion without displacements. Time decay of global solution will be also shown.