96 citations · 400 across the 39 of their papers we have counts for
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math.AP2010★ 14 cited
Spikes and diffusion waves in one-dimensional model of chemotaxis
Grzegorz Karch, Kanako Suzuki
We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity with a given k…
math.AP2010★ 9 cited
Blow-up versus global existence of solutions to aggregation equations
Grzegorz Karch, Kanako Suzuki
A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. Optimal conditions on an interaction potential are obtained which lead e…
math.AP2010★ 3 cited
Barenblatt profiles for a nonlocal porous media equation
Piotr Biler, Cyril Imbert, Grzegorz Karch
We study a generalization of the porous medium equation involving nonlocal terms. More precisely, explicit self-similar solutions with compact support generalizing the Barenblatt s…