Propagation reversal on trees in the large diffusion regime
article
In this work we study travelling wave solutions to bistable reaction–diffusion equations on bi-infinite k-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction–diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formulas to bound the thin region in parameter space where the propagation direction undergoes a reversal. © 2024 The Author(s)
Topics
Lattice differential equationsPropagation reversalReaction–diffusion equationsTravelling wavesTree graphsWave pinningControl nonlinearitiesPartial differential equationsTrees (mathematics)Wave transmissionBistablesDiffusion regimesK-ary treeLattice differential equationPropagation reversalReaction diffusion equationsTraveling wave solutionTree graphDiffusion
TNO Identifier
996982
ISSN
25900374
Source
Results in Applied Mathematics, 23
Files
To receive the publication files, please send an e-mail request to TNO Repository.