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Metric methods for heteroclinic connections
Author(s) -
Monteil Antonin,
Santambrogio Filippo
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4072
Subject(s) - geodesic , mathematics , action (physics) , metric (unit) , mathematical analysis , pure mathematics , operations management , physics , quantum mechanics , economics
We consider the problem min ∫ R1 2 | γ ̇| 2 + W ( γ ) d t among curves connecting two given wells of W ≥0, and we reduce it, following a standard method, to a geodesic problem of the form min ∫ 0 1 K ( γ ) | γ ̇ | d t with K = 2 W . We then prove existence of curves minimizing this new action just by proving that the distance induced by K is proper (i.e., its closed balls are compact). The assumptions on W are minimal, and the method seems robust enough to be applied in the future to some PDE problems. Copyright © 2016 John Wiley & Sons, Ltd.