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), 1748 - 1786.

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.

Siehe englisches Abstract.

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

http://dx.doi.org/10.1080/03605302.2015.1043558

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