Global and exploding solutions for nonlocal quadratic evolution problems

被引：80
|
作者：
Biler, P
Woyczynski, WA
机构：
[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland
[2] Case Western Reserve Univ, Dept Stat, Cleveland, OH 44106 USA
[3] Case Western Reserve Univ, Ctr Stochast & Chaot Proc Sci & Technol, Cleveland, OH 44106 USA
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 1998年 / 59卷 / 03期
关键词：
nonlinear nonlocal parabolic equations; fractal anomalous diffusion; asymptotic behavior of solutions; self-similar solutions;
D O I：
10.1137/S0036139996313447
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data.
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页码：845 / 869
页数：25
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