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

VL - 186

SP - 586

EP - 610

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -