Propagation Reversal for Bistable Differential Equations on Trees

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F23%3A43969593" target="_blank" >RIV/49777513:23520/23:43969593 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/10.1137/22M1502203" target="_blank" >https://epubs.siam.org/doi/10.1137/22M1502203</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/22M1502203" target="_blank" >10.1137/22M1502203</a>

Result language
angličtina
Original language name
Propagation Reversal for Bistable Differential Equations on Trees
Original language description
We study traveling wave solutions to bistable differential equations on infinite k-ary trees. These graphs generalize the notion of classical square infinite lattices and our results complement those for bistable lattice equations on ℤ. Using comparison principles and explicit lower and upper solutions, we show that wave solutions are pinned for small diffusion parameters. Upon increasing the diffusion, the wave starts to travel with nonzero speed, in a direction that depends on the detuning parameter. However, once the diffusion is sufficiently strong, the wave propagates in a single direction up the tree irrespective of the detuning parameter. In particular, our results imply that changes to the diffusion parameter can lead to a reversal of the propagation direction.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA22-18261S" target="_blank" >GA22-18261S: Nonlinear problems with non-standard diffusion</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)