Alexandre Boritchev

most citedLarge global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions

9 citations · 9 across the 2 of their papers we have counts for

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math.AP2022★ 9 cited

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 $R^{d}, d \geq 2$ . We prove that initial data of arbitrary size give rise to global solutions provide…

math.AP2020

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 $u_{t} - ε Δ u + \nabla \cdot (u \nabla K^{*} u) = 0$ in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we…

math.AP2020

Concentration phenomena in a diffusive aggregation model

Piotr Biler, Alexandre Boritchev, Grzegorz Karch +1

We consider the drift-diffusion equation $u_{t} - ε Δ u + \nabla \cdot (u \nabla K ⋆ u) = 0$ in the whole space with global-in-time bounded solutions. Mass concentration pheno…