Approximate Controllability of a Semilinear Heat Equation

By Hugo Leiva, Nelson Merentes, J. Sánchez. 2013

158 citations recorded by the source corpus.

We apply Rothe’s type fixed point theorem to prove the interior approximate controllability of the following semilinear heat equation: in on , where is a bounded domain in , , is an open nonempty subset of , denotes the characteristic function of the set , the distributed control belongs to , and the nonlinear function is smooth enough, and there are , and such that for all Under this condition, we prove the following statement: for all open nonempty subset of , the system is approximately controllable on . Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state to an neighborhood of the final state at time .

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ec0a1e02538fd925382e044c365ff788e78f5f28

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Numerical null controllability of semi-linear 1-D heat equations: Fixed point, least squares and Newton methods (2012, background): “The system (1) is said to be null-controllable at time T if, for any y0 ∈ L2(0, 1) and any globally defined bounded trajectory y?”
Quantitative approximation properties for the fractional heat equation (2017, background): “for instance [11, 13, 27, 25, 31, 32, 33, 41] and in particular [2, 30, 29] for the setting of non-local equations and the references therein), in the present article, motivated by applications to inverse problems, we seek to approximate a given function at each time slice by choosing suitable exter”
The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials (2011, background): “, in the case n = 1 (see for instance [11, 12, 28, 10, 24, 16, 15]).”
Null controllability of Grushin-type operators in dimension two (2011, background): “The null and approximate controllability of the heat equation are essentially well understood subjects for both linear and semilinear equations, and for bounded or unbounded domains (see, for instance, [15], [19], [21], [22], [23], [27], [31], [32], [36], [39], [40], [45], [46]).”