Abstract
This chapter returns to the general W(x) and describes the fact that the varia-tional structure F defined on Pλ and that of Jλ on V = dom(A1/2) stated in Chapter 6 are equivalent up to Morse indices. This fact was known concerning the stability in the case that A is equal to - Δ with the Dirichlet boundary condition, but actually general theory holds true. This structure is not restricted to the Keller-Segel system; it is valid for several mean field theories.
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© 2005 Birkhäuser Boston
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(2005). Dynamical Equivalence. In: Suzuki, T. (eds) Free Energy and Self-Interacting Particles. Progress in Nonlinear Differential Equations and Their Applications, vol 62. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4436-9_9
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DOI: https://doi.org/10.1007/0-8176-4436-9_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4302-7
Online ISBN: 978-0-8176-4436-9
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