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Dual Variational Approach to Nonlinear Diffusion Equations



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Éditeur :

Birkhäuser


Paru le : 2023-03-28



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Description

This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical modelsto various real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.
Pages
212 pages
Collection
n.c
Parution
2023-03-28
Marque
Birkhäuser
EAN papier
9783031245824
EAN PDF
9783031245831
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
21
Taille du fichier
5315 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
137,14 €
EAN EPUB
9783031245831
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
21
Taille du fichier
16763 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
137,14 €
Gabriela Marinoschi is a senior scientific researcher with Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy and full member of the Romanian Academy. Her research interests focus on the analysis and control of evolution equations in infinite dimensional spaces and include the application of variational and semigroup methods as well as the control techniques to mathematical models based on partial differential equations, especially for those describing physical and biological processes.

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