96 citations · 304 across the 18 of their papers we have counts for
23 papers
Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type
Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese
We study two toy models obtained after a slight modification of the nonlinearity of the usual doubly parabolic Keller-Segel system. For these toy models, both consisting of a syste…
Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions
Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese
We study the global existence of the parabolic-parabolic Keller-Segel system in . We prove that initial data of arbitrary size give rise to global solutions provide…
Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation
Piotr Biler, Alexandre Boritchev, Grzegorz Karch +1
We consider the drift-diffusion equation in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we…
Concentration phenomena in a diffusive aggregation model
Piotr Biler, Alexandre Boritchev, Grzegorz Karch +1
We consider the drift-diffusion equation in the whole space with global-in-time bounded solutions. Mass concentration pheno…
Large self-similar solutions of the parabolic-elliptic Keller--Segel model
Piotr Biler, Grzegorz Karch, Hiroshi Wakui
We construct radial self-similar solutions of the, so called, minimal parabolic-elliptic Keller--Segel model in several space dimensions with radial, nonnegative initial conditions…
Blowup of solutions for nonlinear nonlocal heat equations
Piotr Biler
Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutio…