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《数学年刊B辑(英文版)》 2002-04
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THE NAGUMO EQUATION ON SELF-SIMILAR FRACTAL SETS

HU JIAXINDepartment of Mathematics, Tsinghua University, Beijing 100084, China.  
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.
【Key Words】: Fractal set Spectral dimension Sobolev-type inequality Strong (Weak) solution
【CateGory Index】: O175.29
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 LI Jun ping 1,LI Xue wei 2 (1.Research Department, Changsha Railway University, Hunan Changsha, 410075,China; 2.College of Eonomics and Management, Northern Jiaotong University, Beijing 100044,China);The Harmonic Calculus and Brownian Motion on Sierpinski Gasket[J];JOURNAL OF NORTHERN JIAOTONG UNIVERSITY;2000-03
2 LI Xue wei 1,LI Jun ping 2 (1.College of Economics and Management, Northern Jiaotong University, Beijing 100044,China; 2.Research Department, Changsha Railway University, Hunan Changsha, 410075, China);Transition Density for Brownian Motion on SG(2,3)[J];JOURNAL OF NORTHERN JIAOTONG UNIVERSITY;2000-03
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7 GUO Junyi (Department of Mathematics,Nankai University, Tianjin 300071, China);Local extinction of super-Brownian motion on Sierpinski gasket[J];中国科学A辑(英文版);1998-03
8 GUO Junyi Department of Mathematics, Nankai University, Tianjin 300071, China;The oscillation of the occupation time process of super- Brownian motion on Sierpinski gasket[J];中国科学A辑(英文版);2000-12
9 HU Jiaxin Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;Multiple solutions for a class of nonlinear elliptic equations on the Sierpinski gasket[J];中国科学A辑(英文版);2004-05
10 OU Di-fei(HUNan Material School,Changsha 410000);A class of random walks on a nonsymmetric fracfal structure[J];Journal of Lingling Teachers College;2000-03
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