Gabriela Marinoschi's Books

Dual Variational Approach to Nonlinear Diffusion Equations

By: Gabriela Marinoschi

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Dual Variational Approach to Nonlinear Diffusion Equations

By: Gabriela Marinoschi

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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Page Count

223

Publisher

Springer Nature

Published Date

ISBN 10

3031245830

ISBN 13

9783031245831

Degenerate Nonlinear Diffusion Equations

By: Angelo Favini,Gabriela Marinoschi

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Degenerate Nonlinear Diffusion Equations

By: Angelo Favini,Gabriela Marinoschi

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

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Page Count

165

Publisher

Springer

Published Date

ISBN 10

3642282857

ISBN 13

9783642282850

Degenerate Nonlinear Diffusion Equations

By: Angelo Favini,Gabriela Marinoschi

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Degenerate Nonlinear Diffusion Equations

By: Angelo Favini,Gabriela Marinoschi

Average ratings

N/A

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Solve jigsaw puzzle

Age

Page Count

165

Publisher

Springer

Published Date

ISBN 10

3642282857

ISBN 13

9783642282850

Book's by Gabriela Marinoschi

Dual Variational Approach to Nonlinear Diffusion Equations

Dual Variational Approach to Nonlinear Diffusion Equations

Degenerate Nonlinear Diffusion Equations

Degenerate Nonlinear Diffusion Equations

Degenerate Nonlinear Diffusion Equations

Degenerate Nonlinear Diffusion Equations

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