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Null controllability for semilinear heat equation with dynamic boundary conditions

  • * Corresponding author: Omar Oukdach

    * Corresponding author: Omar Oukdach
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  • This paper deals with the null controllability of the semilinear heat equation with dynamic boundary conditions of surface diffusion type, with nonlinearities involving drift terms. First, we prove a negative result for some function $ F $ that behaves at infinity like $ |s| \ln ^{p}(1+|s|), $ with $ p > 2 $. Then, by a careful analysis of the linearized system and a fixed point method, a null controllability result is proved for nonlinearties $ F(s, \xi) $ and $ G(s, \xi) $ growing slower than $ |s| \ln ^{3 / 2}(1+|s|+\|\xi\|)+\|\xi\| \ln^{1 / 2}(1+|s|+\|\xi\|) $ at infinity.

    Mathematics Subject Classification: Primary: 93Bxx; Secondary: 35K05.


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