@article{1461928,
      recid = {1461928},
      author = {Marinoschi, Gabriela.},
      title = {Dual variational approach to nonlinear diffusion equations  /},
      publisher = {Birkhäuser,},
      address = {Cham :},
      pages = {1 online resource (223 p.).},
      year = {2023},
      abstract = {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.},
      url = {http://library.usi.edu/record/1461928},
      doi = {https://doi.org/10.1007/978-3-031-24583-1},
}