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math.AP2020★ 1 cited
Nonlinear Einstein paradigm of Brownian motion and localization property of solutions
Ivan C. Christov, Isanka Garli Hevage, Akif Ibraguimov +1
We employ a generalization of Einstein's random walk paradigm for diffusion to derive a class of multidimensional degenerate nonlinear parabolic equations in non-divergence form. S…
math.AP2020★ 3 cited
Long-time asymptotics of non-degenerate non-linear diffusion equations
Ivan C. Christov, Akif Ibraguimov, Rahnuma Islam
We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negati…