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Multiplicative controllability for reaction-diffusion equations with target states admitting finitely many changes of sign. (English) Zbl 1219.93010
Summary: 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.

MSC:
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
35K10 Second-order parabolic equations
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