17,663 research outputs found
On a nonlocal degenerate parabolic problem
Conditions for the existence and uniqueness of weak solutions for a class of
nonlinear nonlocal degenerate parabolic equations are established. The
asymptotic behaviour of the solutions as time tends to infinity are also
studied. In particular, the finite time extinction and polynomial decay
properties are proved
Diluted antiferromagnet in a ferromagnetic enviroment
The question of robustness of a network under random ``attacks'' is treated
in the framework of critical phenomena. The persistence of spontaneous
magnetization of a ferromagnetic system to the random inclusion of
antiferromagnetic interactions is investigated. After examing the static
properties of the quenched version (in respect to the random antiferromagnetic
interactions) of the model, the persistence of the magnetization is analysed
also in the annealed approximation, and the difference in the results are
discussed
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