ISSN:
1572-9265
Schlagwort(e):
bifurcation function
;
elliptic boundary value problem
;
finite element method
;
reduction to an alternative problem
;
stability of steady-states
;
35J25
;
65N35
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Informatik
,
Mathematik
Notizen:
Abstract Solutions $$u \in H_0^1 (\Omega ) \cap H^2 (\Omega )$$ of a semilinear elliptic boundary value problem, $$Au + f(x,u,\lambda ) = 0$$ (with $$f_u (x,u,\lambda )$$ bounded below) can be put into a one-to-one correspondence with zeros $$c \in \mathbb{R}^d $$ of a function $$c \to B(c,\lambda ) \in \mathbb{R}^d $$ . Often d is small. The function $$B(c,\lambda )$$ is called the bifurcation function. It can also be shown that the eigenvalues of the matrix $$B_c (c,\lambda )$$ characterize the stability properties of the solutions of the elliptic problem as rest points of $$u_t + Au + f(x,u,\lambda ) = 0$$ . A finite element method that can be used for computing B and B c has recently been proposed. An overview of these results and the finite element method is given.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1019117130906
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