Unique continuation for solutions of a timoshenko's equation

Abstract

We prove that the solutions of a dynamial Timoshenko type equation enjoy the so-called Unique Continuation Property. The result is established using Carleman type estimates for a differential operator which appears naturally in the discussion of our problem. An inequality due to F. Treves plays a central role in our discussion.

Keywords:

• Unique continuations
• Timoshenko's equation
• Carleman type estimates

¹Department of Mathematics, FUNREI, Säo Jäo del Rei - MG, Brazil and Universidad Nacional de Ingenieria, Lima, Perú.

²National Laboratory of Scientific Computation, LNCC/CNP_q and Federal University of Rio de Janeiro, RJ, Brazil. [email protected]

¹Department of Mathematics, FUNREI, Säo Jäo del Rei - MG, Brazil and Universidad Nacional de Ingenieria, Lima, Perú.

²National Laboratory of Scientific Computation, LNCC/CNP_q and Federal University of Rio de Janeiro, RJ, Brazil. [email protected]

Notes

¹Department of Mathematics, FUNREI, Säo Jäo del Rei - MG, Brazil and Universidad Nacional de Ingenieria, Lima, Perú.

²National Laboratory of Scientific Computation, LNCC/CNP_q and Federal University of Rio de Janeiro, RJ, Brazil. [email protected]