48 citations · 178 across the 24 of their papers we have counts for
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math.DS2015
Nonlocally maximal and premaximal hyperbolic sets
T. Fisher, T. Petty, S. Tikhomirov
We prove that for any closed manifold of dimension 3 or greater that there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one.…
math.AP2015
Recent Advances in Reaction-Diffusion Equations with Non-Ideal Relays
Mark Curran, Pavel Gurevich, Sergey Tikhomirov
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a relate…
math.AP2015★ 7 cited
Spatially discrete reaction-diffusion equations with discontinuous hysteresis
Pavel Gurevich, Sergey Tikhomirov
We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable an…