Dual Variational Approach to Nonlinear Diffusion Equations (Hardcover, 1st ed. 2023)

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

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	PNLDE Subseries in Control, 102
Release date:	March 2023
First published:	2023
Authors:	Gabriela Marinoschi
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	212
Edition:	1st ed. 2023
ISBN-13:	978-3-03-124582-4
Categories:	Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Books > Science & Mathematics > Mathematics > Optimization > General
LSN:	3-03-124582-2
Barcode:	9783031245824

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