Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

Numerics for the Control of Partial Differential Equations

  • Enrique Zuazua
Reference work entry
DOI: https://doi.org/10.1007/978-3-540-70529-1_362


Control theory is now an old subject. It emerged with the Industrial Revolution and has been continuously evolving since. New technological and industrial processes and mechanisms need new control strategies, and this leads to new Mathematics of Control as well. At present control theory is certainly one of the most interdisciplinary areas of research, and it arises vigorously in most modern applications.

Since its origins (see [3, 12]) the field has evolved tremendously, and different tools have been developed to face the main challenges that require to deal with a variety of models: Ordinary Differential Equations/Partial Differential Equations, Linear/Nonlinear, Deterministic/Stochastic, etc.

Practical control problems can be formulated in many different ways, requiring different kinds of answers, related to the different notions of control; the various possible modeling paradigms; and the degree of precision of the result one is looking for optimal control,...

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Partially supported by the ERC Advanced Grant FP7-246775 NUMERIWAVES, the Grant PI2010-04 of the Basque Government, the ESF Research Networking Program OPTPDE and Grant MTM2011-29306 of the MINECO, Spain.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Enrique Zuazua
    • 1
    • 2
  1. 1.BCAM – Basque Center for Applied MathematicsBilbaoSpain
  2. 2.Ikerbasque – Basque Foundation for ScienceBilbaoSpain