24 citations · 122 across the 27 of their papers we have counts for
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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…
Asymptotics of parabolic Green's functions on lattices
Pavel Gurevich
For parabolic spatially discrete equations, we consider Green's functions, also known as heat kernels on lattices. We obtain their asymptotic expansions with respect to powers of t…
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…
Asymptotics of sign-changing patterns in hysteretic systems with diffusive thresholds
Pavel Gurevich, Dmitrii Rachinskii
We consider a reaction-diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evo…
Pattern formation in parabolic equations containing hysteresis with diffusive thresholds
Pavel Gurevich, Dmitrii Rachinskii
We consider a reaction-diffusion system with discontinuous reaction terms modeled by non-ideal relays. The system is motivated by an epigenetic population model of evolution of two…
Well-posedness of parabolic equations containing hysteresis with diffusive thresholds
Pavel Gurevich, Dmitrii Rachinskii
We study complex systems arising, in particular, in population dynamics, developmental biology, and bacterial metabolic processes, in which each individual element obeys a relative…