TY - JOUR
T1 - Exponential separation and principal floquet bundles for linear parabolic equations on ℝN
AU - Húska, Juraj
AU - Poláčik, Peter
PY - 2008/1
Y1 - 2008/1
N2 - We consider linear nonautonomous second order parabolic equations on ℝN. Under an instability condition, we prove the existence of two complementary Floquet bundles, one spanned by a positive entire solution - the principal Floquet bundle, the other one consisting of sign-changing solutions. We establish an exponential separation between the two bundles, showing in particular that a class of sign-changing solutions are exponentially dominated by positive solutions.
AB - We consider linear nonautonomous second order parabolic equations on ℝN. Under an instability condition, we prove the existence of two complementary Floquet bundles, one spanned by a positive entire solution - the principal Floquet bundle, the other one consisting of sign-changing solutions. We establish an exponential separation between the two bundles, showing in particular that a class of sign-changing solutions are exponentially dominated by positive solutions.
KW - Exponential separation
KW - Parabolic equations on ℝ
KW - Positive entire solutions
KW - Principal Floquet bundle
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U2 - 10.3934/dcds.2008.20.81
DO - 10.3934/dcds.2008.20.81
M3 - Article
AN - SCOPUS:41649095716
SN - 1078-0947
VL - 20
SP - 81
EP - 113
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 1
ER -