THE NAGUMO EQUATION ON SELF-SIMILAR FRACTAL SETS

被引:0
作者
HU JIAXINDepartment of Mathematics Tsinghua University Beijing China [100084 ]
机构
关键词
Fractal set; Spectral dimension; Sobolev-type inequality; Strong (Weak) solution;
D O I
暂无
中图分类号
O175.29 [非线性偏微分方程];
学科分类号
070104 ;
摘要
<正>The Nagumo equationut = △u+bu(u-a)(1-u), t>0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the "pathological" property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.
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页码:519 / 530
页数:12
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