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Nonlinear theories --- Numerical analysis --- Business, Economy and Management --- Mathematical Sciences --- Economics --- Applied Mathematics --- Mathematics --- Mathematical physics --- Physics --- Mathematical physics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Analyse fonctionnelle non linéaire --- Anàlisi funcional no lineal. --- Equacions diferencials no lineals. --- Revistes electròniques.

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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.

Differential equations. --- System theory. --- Control theory. --- Operator theory. --- Mathematical optimization. --- Calculus of variations. --- Differential Equations. --- Systems Theory, Control . --- Operator Theory. --- Calculus of Variations and Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Functional analysis --- Dynamics --- Machine theory --- Systems, Theory of --- Systems science --- Science --- 517.91 Differential equations --- Differential equations --- Philosophy --- Burgers equation. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Diffusion equation, Nonlinear --- Heat flow equation, Nonlinear --- Nonlinear diffusion equation --- Nonlinear heat flow equation --- Heat equation --- Navier-Stokes equations --- Turbulence --- Equacions diferencials no lineals