TY - GEN digital ID - 131914563 TI - Dual Variational Approach to Nonlinear Diffusion Equations PY - 2023 SN - 9783031245831 9783031245824 9783031245848 9783031245855 PB - Cham Springer Nature Switzerland :Imprint: Birkhäuser DB - UniCat KW - Operator theory KW - Functional analysis KW - Differential equations KW - Numerical methods of optimisation KW - Operational research. Game theory KW - differentiaalvergelijkingen KW - analyse (wiskunde) KW - systeemtheorie KW - wiskunde KW - kansrekening KW - optimalisatie UR - https://www.unicat.be/uniCat?func=search&query=sysid:131914563 AB - 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. ER -