Dual Variational Approach to Nonlinear Diffusion Equations (Progress in Nonlinear Differential Equations and Their Applications, 102, Band 102) - Hardcover

Marinoschi, Gabriela

Hardcover

ISBN 10: 3031245822 ISBN 13: 9783031245824

Verlag: Birkhäuser, 2023

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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 models tovarious real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2023
• Sprache: Englisch
• ISBN 10: 3031245822
• ISBN 13: 9783031245824
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 230
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland