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Dual variational approach to nonlinear diffusion equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dual variational approach to nonlinear diffusion equationsby Gabriela Marinoschi.
Author:	Marinoschi, Gabriela.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xviii, 212 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Nonlinear.
Online resource:	https://doi.org/10.1007/978-3-031-24583-1
ISBN:	9783031245831$q(electronic bk.)

Dual variational approach to nonlinear diffusion equations
Marinoschi, Gabriela.

Dual variational approach to nonlinear diffusion equations[electronic resource] /by Gabriela Marinoschi. - Cham :Springer Nature Switzerland :2023. - xviii, 212 p. :ill., digital ;24 cm. - Progress in nonlinear differential equations and their applications ;v. 102. - Progress in nonlinear differential equations and their applications ;v.83..

Introduction -- Nonlinear Diffusion Equations with Slow and Fast Diffusion -- Weakly Coercive Nonlinear Diffusion Equations -- Nonlinear Diffusion Equations with a Noncoercive Potential -- Nonlinear Parabolic Equations in Divergence Form with Wentzell Boundary Conditions -- A Nonlinear Control Problem in Image Denoising -- An Optimal Control Problem for a Phase Transition Model -- Appendix -- Bibliography -- Index.

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.

ISBN: 9783031245831$q(electronic bk.)

Standard No.: 10.1007/978-3-031-24583-1doiSubjects--Topical Terms:

185178
Differential equations, Nonlinear.

LC Class. No.: QA372

Dewey Class. No.: 515.355

Dual variational approach to nonlinear diffusion equations
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245 1 0 $a Dual variational approach to nonlinear diffusion equations $h [electronic resource] / $c by Gabriela Marinoschi.
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490 1 $a Progress in nonlinear differential equations and their applications ; $v v. 102
505 0 $a Introduction -- Nonlinear Diffusion Equations with Slow and Fast Diffusion -- Weakly Coercive Nonlinear Diffusion Equations -- Nonlinear Diffusion Equations with a Noncoercive Potential -- Nonlinear Parabolic Equations in Divergence Form with Wentzell Boundary Conditions -- A Nonlinear Control Problem in Image Denoising -- An Optimal Control Problem for a Phase Transition Model -- Appendix -- Bibliography -- Index.
520 $a 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.
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650 2 4 $a Calculus of Variations and Optimization. $3 913393
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830 0 $a Progress in nonlinear differential equations and their applications ; $v v.83. $3 558793
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