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arXiv · 1612.08774

Local null controllability for degenerate parabolic equations with nonlocal term

Reginaldo Demarque·Juan Límaco·Luiz Viana
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Abstract

We establish a local null controllability result for following the nonlinear parabolic equation: $$u_t-\left(b\left(x,\int_0^1u \ \right)u_x \right)_x+f(t,x,u)=h\chi_\omega,\ (t,x)\in (0,T)\times (0,1) $$ where $b(x,r)=\ell(r)a(x)$ is a function with separated variables that defines an operator which degenerates at $x=0$ and has a nonlocal term. Our approach relies on an application of Liusternik's inverse mapping theorem that demands the proof of a suitable Carleman estimate.

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Reginaldo Demarque, Juan Límaco, Luiz Viana. 2016-12-28. Local null controllability for degenerate parabolic equations with nonlocal term. https://doi.org/10.1016/j.nonrwa.2018.04.001

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