Dual Variational Approach to Nonlinear Diffusion Equations: 102 (Progress in Nonlinear Differential Equations and Their Applications, 102) - Tapa dura
Sinopsis
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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Acerca del autor
Gabriela Marinoschi is a senior scientific researcher with Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy and full member of the Romanian Academy. Her research interests focus on the analysis and control of evolution equations in infinite dimensional spaces and include the application of variational and semigroup methods as well as the control techniques to mathematical models based on partial differential equations, especially for those describing physical and biological processes.
De la contraportada
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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Dual Variational Approach to Nonlinear Diffusion Equations (Progress in Nonlinear Differential Equations and Their Applications, 102)
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Dual Variational Approach to Nonlinear Diffusion Equations (eng)
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Dual Variational Approach to Nonlinear Diffusion Equations (Progress in Nonlinear Differential Equations and Their Applications, 102)
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Dual Variational Approach to Nonlinear Diffusion Equations (Progress in Nonlinear Differential Equations and Their Applications, 102)
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Dual Variational Approach to Nonlinear Diffusion Equations
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Springer Nature Switzerland Mrz 2023, 2023
ISBN 10: 3031245822
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 232 pp. Englisch. Nº de ref. del artículo: 9783031245824
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Dual Variational Approach to Nonlinear Diffusion Equations
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Condición: Hervorragend. Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | 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. Nº de ref. del artículo: 41585995/1
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Dual Variational Approach to Nonlinear Diffusion Equations
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ISBN 10: 3031245822
ISBN 13: 9783031245824
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Gebunden. Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Presents technique for proving existence of solutions to nonlinear diffusion equationsUtilizes specific examples that can model real-world physical processesChapters develop methods for treating particular important casesGabriela. Nº de ref. del artículo: 770364534
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Dual Variational Approach To Nonlinear D
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Dual Variational Approach to Nonlinear Diffusion Equations
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ISBN 10: 3031245822
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Buch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 232 pp. Englisch. Nº de ref. del artículo: 9783031245824
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Dual Variational Approach to Nonlinear Diffusion Equations: 102 (Progress in Nonlinear Differential Equations and Their Applications)
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