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

Dual Variational Approach to Nonlinear Diffusion Equations (PNLDE Subseries in Control) PDF

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