TY - JOUR
T1 - Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations
AU - Akagi, Goro
AU - Kajikiya, Ryuji
PY - 2013/7
Y1 - 2013/7
N2 - Every solution u = u(x, t) of the Cauchy-Dirichlet problem for the fast diffusion equation, ∂ t ({pipe}u{pipe}m-2 u) = Δu in Ω × (0, ∞) with a smooth bounded domain Ω of ℝN and 2 < m < 2*: = 2N/(N - 2)+, vanishes in finite time at a power rate. This paper is concerned with asymptotic profiles of sign-changing solutions and a stability analysis of the profiles. Our method of proof relies on a detailed analysis of a dynamical system on some surface in the usual energy space as well as energy method and variational method.
AB - Every solution u = u(x, t) of the Cauchy-Dirichlet problem for the fast diffusion equation, ∂ t ({pipe}u{pipe}m-2 u) = Δu in Ω × (0, ∞) with a smooth bounded domain Ω of ℝN and 2 < m < 2*: = 2N/(N - 2)+, vanishes in finite time at a power rate. This paper is concerned with asymptotic profiles of sign-changing solutions and a stability analysis of the profiles. Our method of proof relies on a detailed analysis of a dynamical system on some surface in the usual energy space as well as energy method and variational method.
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U2 - 10.1007/s00229-012-0583-9
DO - 10.1007/s00229-012-0583-9
M3 - Article
AN - SCOPUS:84878757592
SN - 0025-2611
VL - 141
SP - 559
EP - 587
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 3-4
ER -