Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms

By V. Cabanillas, S. B. de Menezes, Enrique Zuazua. 2001

56 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/329745cff2d02281d3c8f99221df141c18f037f0

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Regional controllability of semilinear degenerate parabolic equations in bounded domains (2006, methodology): “To prove the controllability results we will use, as in [4], a fixed point method.”
Some results on controllability for linear and nonlinear heat equations in unbounded domains (2007, methodology): “The structure of the proof (the controllability of a similar linear system together with a fixed point argument) is rather general and has been used in several previous works, for instance, in [27], [6], [10], [1], [3], etc.”
Null controllability of degenerate heat equations (2005, background): “Introduction Controllability properties of nondegenerate parabolic equations have been widely studied in recent years; concerning the heat equation, see in particular [2, 6, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 34, 35, 37, 38]; concerning the Stokes and Navier-Stokes equations, see in”
CONTROLLABILITY OF PARTIAL DIFFERENTIAL EQUATIONS AND ITS SEMI-DISCRETE APPROXIMATIONS (2006, background): “In this geometrical setting the null controllability property was proved in [14].”
Observable set, observability, interpolation inequality and spectral inequality for the heat equation in Rn (2017, background): “) About works on sufficient conditions of observable sets for heat equations in unbounded domains, we would like to mention the work [7].”
Carleman estimates for one-dimensional degenerate heat equations (2006, background): “As in [4, 5], using the method of [26], the results of the present paper also show the null controllability of the Crocco equation for general functions a.”