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Quasilinear degenerate parabolic equations of Kirchhoff type

โœ Scribed by Massimo Gobbino

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
123 KB
Volume
22
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

We investigate the evolution problem u#m("Au")Au"0, u(

where H is a Hilbert space, A is a self-adjoint linear non-negative operator on H with domain D(A), and

We prove that if u 3D(A), and m("Au ")O0, then there exists at least one global solution, which is unique if either m never vanishes, or m is locally Lipschitz continuous.

Moreover, we prove that if (1# )m( )*c'0 for all *0, then this problem is well posed in H. On the contrary, if for some '1 it happens that (1# ?)m( ))c(# R for all *0, then this problem has no solution if u , D(A@) with small enough. We apply these results to degenerate parabolic PDEs with non-local non-linearities.

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