Overview
- Presents technique for proving existence of solutions to nonlinear diffusion equations
- Utilizes specific examples that can model real-world physical processes
- Chapters develop methods for treating particular important cases
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 102)
Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Dual Variational Approach to Nonlinear Diffusion Equations
Authors: Gabriela Marinoschi
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-031-24583-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-24582-4Published: 29 March 2023
Softcover ISBN: 978-3-031-24585-5Published: 30 March 2024
eBook ISBN: 978-3-031-24583-1Published: 28 March 2023
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XVIII, 212
Topics: Analysis, Systems Theory, Control, Operator Theory, Optimization