Dual Variational Approach to Nonlinear Diffusion Equations
indgår i PNLDE Subseries in Control serien
- Indbinding:
- Hardback
- Sideantal:
- 232
- Udgivet:
- 29. marts 2023
- Udgave:
- 23001
- Størrelse:
- 160x19x241 mm.
- Vægt:
- 518 g.
- 8-11 hverdage.
- 21. november 2024
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Beskrivelse af Dual Variational Approach to Nonlinear Diffusion Equations
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.
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Bogen Dual Variational Approach to Nonlinear Diffusion Equations findes i følgende kategorier:
- Business og læring
- Reference, information og tværfaglige emner > Forskning og information: generelt > Informationsteori > Kybernetik og systemteori
- Matematik og naturvidenskab > Matematik > Regning og matematisk analyse > Funktionsanalyse og transformation
- Matematik og naturvidenskab > Matematik > Regning og matematisk analyse > Differentialregning og differentialligninger
- Matematik og naturvidenskab > Matematik > Optimalisering
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