TY - JOUR
T1 - Braided connecting orbits in parabolic equations via computational homology
AU - van den Berg, G.J.B.
AU - Day, S.L.
AU - van der Vorst, R.C.A.M.
PY - 2013
Y1 - 2013
N2 - We develop and present a computational method for producing forcing theorems for stationary and periodic solutions and con-necting orbits in scalar parabolic equations with periodic boundary conditions. This method is based on prior work by van den Berg, Ghrist, and Vandervorst on a Conley index theory for solutions braided through a collection of known stationary solutions. Essen-tially, the topological structure of the stationary solutions forces the existence of additional solutions with a specified topological type. In particular, this paper studies connecting orbits and devel-ops and implements the algorithms required to compute the index, providing sample results as illustrations. © 2013 Elsevier Inc.
AB - We develop and present a computational method for producing forcing theorems for stationary and periodic solutions and con-necting orbits in scalar parabolic equations with periodic boundary conditions. This method is based on prior work by van den Berg, Ghrist, and Vandervorst on a Conley index theory for solutions braided through a collection of known stationary solutions. Essen-tially, the topological structure of the stationary solutions forces the existence of additional solutions with a specified topological type. In particular, this paper studies connecting orbits and devel-ops and implements the algorithms required to compute the index, providing sample results as illustrations. © 2013 Elsevier Inc.
U2 - 10.1016/j.jde.2013.05.007
DO - 10.1016/j.jde.2013.05.007
M3 - Article
SN - 0022-0396
VL - 255
SP - 1086
EP - 1108
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -