A. Jüngel, M. Winkler:
"A Degenerate Fourth-Order Parabolic Equation Modeling Bose-Einstein Condensation. Part I: Local Existence of Solutions";
Archive for Rational Mechanics and Analysis, 217 (2015), S. 935 - 973.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
A degenerate fourth-order parabolic equation modeling condensation phenomena
related to Bose-Einstein particles is analyzed. The model is a Fokker-Planck-type
approximation of the Boltzmann-Nordheim equation, only keeping the leading
order term. It maintains some of the main features of the kinetic model, namely
mass and energy conservation and condensation at zero energy. The existence of
a local-in-time nonnegative continuous weak solution is proven. If the solution is
not global, it blows up with respect to the L^\infty norm in finite time. The proof is
based on approximation arguments, interpolation inequalities in weighted Sobolev
spaces, and suitable a priori estimates for a weighted gradient L^2 norm.

Higher-order parabolic equations; existence of solutions

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