Titelaufnahme

Titel
Avoiding degeneracy in the Westervelt equation by state constrained optimal control
Verfasser/ VerfasserinClason, Christian ; Kaltenbacher, Barbara
Erschienen in
Evolution Equations and Control Theory, Springfield, MO, 2013, Jg. 2, H. 2, S. 281-300
ErschienenAIMS
Ausgabe
Preprint
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (GND)Optimale Kontrolle / Nichtlineare Akustik / Online-Publikation
URNurn:nbn:at:at-ubg:3-437 Persistent Identifier (URN)
DOIdoi:10.3934/eect.2013.2.281 
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Avoiding degeneracy in the Westervelt equation by state constrained optimal control [0.34 mb]
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Zusammenfassung (Englisch)

The Westervelt equation, which describes nonlinear acoustic wave propagation in high intensity ultrasound applications, exhibits potential degeneracy for large acoustic pressure values. While well-posedness results on this PDE have so far been based on smallness of the solution in a higher order spatial norm, non-degeneracy can be enforced explicitly by a pointwise state constraint in a minimization problem, thus allowing for pressures with large gradients and higher-order derivatives, as is required in the mentioned applications. Using regularity results on the linearized state equation, well-posedness and necessary optimality conditions for the PDE constrained optimization problem can be shown via a relaxation approach by Alibert and Raymond.

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