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Zeitschriftenartikel:

A. Jüngel, M. Winkler:
"A Degenerate Fourth-Order Parabolic Equation Modeling Bose-Einstein Condensation Part II: Finite-Time Blow-Up";
Communications in Partial Differential Equations, 40 (2015), S. 1748 - 1786.

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 can be motivated from
the spatially homogeneous and isotropic Boltzmann-Nordheim equation by a formal
Taylor expansion of the collision integral. It maintains some of the main features of
the kinetic model, namely mass and energy conservation and condensation at zero
energy. The existence of local-in-time weak solutions satisfying a certain entropy
inequality is proven. The main result asserts that if a weighted L^1 norm of the initial
data is sufficiently large and the initial data satisfies some integrability conditions,
the solution blows up with respect to the L^\infty norm in finite time. Furthermore, the
set of all such blow-up enforcing initial functions is shown to be dense in the set
of all admissible initial data. The proofs are based on approximation arguments
and interpolation inequalities in weighted Sobolev spaces. By exploiting the entropy
inequality, a nonlinear integral inequality is proved which implies the finite-time
blow-up property.

Schlagworte:
Higher-order parabolic equations; finite-time blow-up of solutions

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