التفاصيل البيبلوغرافية
| العنوان: |
Large Fronts in Nonlocally Coupled Systems Using Conley–Floer Homology. |
| المؤلفون: |
Bakker, Bente Hilde, van den Berg, Jan Bouwe |
| المصدر: |
Annales Henri Poincaré; Feb2023, Vol. 24 Issue 2, p605-696, 92p |
| مصطلحات موضوعية: |
VECTOR fields, PHASE space, DYNAMICAL systems, MORSE theory, MATHEMATICAL convolutions |
| مستخلص: |
In this paper, we study travelling front solutions for nonlocal equations of the type ∂ t u = N ∗ S (u) + ∇ F (u) , u (t , x) ∈ R d. Here, N ∗ denotes a convolution-type operator in the spatial variable x ∈ R , either continuous or discrete. We develop a Morse-type theory, the Conley–Floer homology, which captures travelling front solutions in a topologically robust manner, by encoding fronts in the boundary operator of a chain complex. The equations describing the travelling fronts involve both forward and backward delay terms, possibly of infinite range. Consequently, these equations lack a natural phase space, so that classic dynamical systems tools are not at our disposal. We therefore develop, from scratch, a general transversality theory, and a classification of bounded solutions, in the absence of a phase space. In various cases the resulting Conley–Floer homology can be interpreted as a homological Conley index for multivalued vector fields. Using the Conley–Floer homology, we derive existence and multiplicity results on travelling front solutions. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
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