TY - JOUR
T1 - Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains
AU - Poláčik, P.
AU - Simondon, F.
PY - 2002/12/10
Y1 - 2002/12/10
N2 - We consider the Dirichlet problem for the semilinear heat equation ut = Δu + g(x, u), xεΩ, where Ω is an arbitrary bounded domain in ℝN, N≥2, with C2 boundary. We find a C∞-function g(x, u) such that (0.1) has a bounded solution whose ω-limit set is a continuum of equilibria. This extends and improves an earlier result of the first author with Rybakowski, in which Ω is a disk in ℝ2 and g is of finite differentiability class. We also show that (0.1) can have an infinite-dimensional manifold of nonconvergent bounded trajectories.
AB - We consider the Dirichlet problem for the semilinear heat equation ut = Δu + g(x, u), xεΩ, where Ω is an arbitrary bounded domain in ℝN, N≥2, with C2 boundary. We find a C∞-function g(x, u) such that (0.1) has a bounded solution whose ω-limit set is a continuum of equilibria. This extends and improves an earlier result of the first author with Rybakowski, in which Ω is a disk in ℝ2 and g is of finite differentiability class. We also show that (0.1) can have an infinite-dimensional manifold of nonconvergent bounded trajectories.
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U2 - 10.1016/S0022-0396(02)00014-1
DO - 10.1016/S0022-0396(02)00014-1
M3 - Article
AN - SCOPUS:0037059083
SN - 0022-0396
VL - 186
SP - 586
EP - 610
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -