Abstract
In this paper, we study the null controllability of weakly degenerateparabolic systems with two different diffusion coefficients and one control force.To obtain this aim, we had to develop new global Carleman estimates for adegenerate parabolic equation, with weight functions different from the ones of [2], [10] and [31].
Highlights
In [2], [10], [32] new Carleman estimates were developed for degenerate parabolic equations and used to show observability inequalities of the adjoint degenerate problems and obtain the null controllability
In [1], we studied the null controllability for degenerate cascade systems with general coupling terms and two different diffusion coefficients
For the coupled system (1.9)-(1.12) we prove first an intermediate important result which could be used to show the null controllability for a coupled system with two control forces
Summary
In [2], [10], [32] new Carleman estimates were developed for degenerate parabolic equations and used to show observability inequalities of the adjoint degenerate problems and obtain the null controllability. In [8], Cannarsa and De Teresa studied the null controllability of cascade degenerate linear systems with the same diffusion coefficient, i.e., α1 = α2, and with the particular coupling term b21 = 1O for some open set O ⊂ (0, 1). In [1], we studied the null controllability for degenerate cascade systems with general coupling terms and two different diffusion coefficients. Semigroups, Carleman estimates, degenerate, parabolic equations, coupled systems, control force, observability inequality, null controllability. We give summarized proofs of Caccioppoli and Hardy-Poincare inequalities
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