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November  2010, 14(4): 1293-1311. doi: 10.3934/dcdsb.2010.14.1293

Multiplicative controllability for reaction-diffusion equations with target states admitting finitely many changes of sign

Piermarco Cannarsa 1, and  Alexander Khapalov 2,

1. 

Department of Mathematics, University of Rome "Tor Vergata", 00133 Rome, Italy
2. 

Department of Mathematics, Washington State University, Pullman, WA 99164-3113, United States

Received  August 2009 Revised  March 2010 Published  August 2010

We study the global approximate controllability properties of a one dimensional reaction-diffusion equation governed via the coefficient of the reaction term. The traditional (linear operator) controllability methods based on the duality pairing do not apply to such a problem. Instead, we focus on the qualitative study of the diffusion and reaction parts of the evolution process at hand. We consider the case when both the initial and target states admit no more than finitely many changes of sign.
Keywords: Multiplicative controllability, parabolic equation, nonlinearity..
Mathematics Subject Classification: Primary: 93C20; Secondary: 35K10, 93B0.
Citation: Piermarco Cannarsa, Alexander Khapalov. Multiplicative controllability for reaction-diffusion equations with target states admitting finitely many changes of sign. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1293-1311. doi: 10.3934/dcdsb.2010.14.1293
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