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In den WarenkorbGebunden. Zustand: New. Unifying approach to different boundary value problems related to diffusion in porous media, in particular to water infiltration in soilsSystematic and rigorous study of diffusion models in porous media within the functional approach.
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Sprache: Englisch
Verlag: Birkhauser Verlag AG, Basel, 2024
ISBN 10: 3031245857 ISBN 13: 9783031245855
Anbieter: Grand Eagle Retail, Bensenville, IL, USA
Paperback. Zustand: new. Paperback. 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. This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.