Calculus of Variations and Geometric Measure Theory
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G. Floridia

Approximate controllability for nonlinear degenerate parabolic problems with bilinear control

created by floridia on 12 Dec 2017



Inserted: 12 dec 2017

Journal: Journal Differential Equations
Volume: 257
Number: 9
Pages: 3382–3422
Year: 2014
Doi: 10.1016/j.jde.2014.06.016

ArXiv: 1406.1447 PDF


In this paper, we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy–Neumann problems. First, we obtain embedding results for weighted Sobolev spaces, that have proved decisive in reaching well-posedness for nonlinear degenerate problems. Then, we show that the above systems can be steered in $L^2$ from any nonzero, nonnegative initial state into any neighborhood of any desirable nonnegative target-state by bilinear piecewise static controls. Moreover, we extend the above result relaxing the sign constraint on the initial data.

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