Global and Exploding Solutions for Nonlocal Quadratic Evolution Problems
Global and Exploding Solutions for Nonlocal Quadratic Evolution Problems
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DOI：
10.1137/s0036139996313447
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发表时间：
1998-12
期刊：
影响因子：
--
通讯作者：
P. Biler;W. Woyczynski
中科院分区：
文献类型：
--
作者：
P. Biler;W. Woyczynski
考虑了非线性非局部抛物方程组对相互作用粒子密度演化的模拟。惯性型非线性是二次的和非局部的，而扩散项也是非局部的，是反常的和分形的，即，由拉普拉斯算子的分数幂表示。研究了系统在时间上整体存在与有限时间爆破的条件。对于一定的齐次初始数据，构造了自相似解。
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.