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Local controllability of a nonlinear wave equation

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Abstract

We obtain results on local controllability (near an equilibrium point) for a nonlinear wave equation, by application of an infinite-dimensional analogue of the Lee-Markus method of linearization. Controllability of the linearized equation is studied by application of results of Russell, and local controllability of the nonlinear equation follows from the inverse function theorem. We prove that every state that is sufficiently small in a sense made precise in the paper can be reached from the origin in a timeT depending on the coefficients of the equation.

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Authors and Affiliations

  1. Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Buenos Aires, Argentina

    H. O. Fattorini

  2. Department of Mathematics, University of California, 90024, Los Angeles, California, USA

    H. O. Fattorini

Authors
  1. H. O. Fattorini
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Additional information

This research was supported in part by the National Science Foundation under contract GP-9658.

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Fattorini, H.O. Local controllability of a nonlinear wave equation. Math. Systems Theory 9, 30–45 (1975). https://doi.org/10.1007/BF01698123

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