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Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form. (English) Zbl 1176.35108

The paper presents null controllability results for some degenerate parabolic equations in non divergence form on a bounded interval. The structure of the paper is as follows. First, the authors prove the well-posedness of the linear system, then for the adjoint problems they obtain Carleman estimates. After that, for the same adjoint system they prove the observability, and as a consequence they give the null controllability result for the considered linear system. In the final part, the authors extend previous results to a semilinear system.

MSC:

35K65 Degenerate parabolic equations
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
93B07 Observability
35K55 Nonlinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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