Corpus ID: 55788761

Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis

@article{Jais2008ClassicalAW,
  title={Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis},
  author={Mathias Jais},
  journal={Opuscula Mathematica},
  year={2008},
  volume={28},
  pages={47-62}
}

Mathias Jais

Published 2008

Mathematics

Opuscula Mathematica

We consider the solvability of the semilinear parabolic differential equation \[\frac{\partial u}{\partial t}(x,t)- \Delta u(x,t) + c(x,t)u(x,t) = \mathcal{P}(u) + \gamma (x,t)\] in a cylinder \(D=\Omega \times (0,T)\), where \(\mathcal{P}\) is a hysteresis operator of Preisach type. We show that the corresponding initial boundary value problems have unique classical solutions. We further show that using this existence and uniqueness result, one can determine the properties of the Preisach… CONTINUE READING

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