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Dual variational approach to nonline...

Marinoschi, Gabriela.

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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 equations/ by Gabriela Marinoschi.
Author:	Marinoschi, Gabriela.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xviii, 212 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Nonlinear. -
Online resource:	https://doi.org/10.1007/978-3-031-24583-1
ISBN:	9783031245831

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. 102..

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

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

604084
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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300 $a xviii, 212 p. : $b ill., digital ; $c 24 cm.
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.
650 0 $a Differential equations, Nonlinear. $3 604084
650 0 $a Burgers equation. $3 709136
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Systems Theory, Control. $3 893834
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Calculus of Variations and Optimization. $3 3538813
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Progress in nonlinear differential equations and their applications ; $v v. 102. $3 3632336
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950 $a Mathematics and Statistics (SpringerNature-11649)