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Evolution Equations and Control Theory / Avoiding degeneracy in the Westervelt equation by state constrained optimal control
- Publication Year :
- 2013
-
Abstract
- 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.
Details
- Database :
- OAIster
- Notes :
- 49-XX, text/html, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1366931622
- Document Type :
- Electronic Resource
- Full Text :
- https://doi.org/10.3934.eect.2013.2.281