4 papers
Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up
Debdip Ganguly, Debabrata Karmakar, Saikat Mazumdar
We consider the following Cauchy problem for the semi linear heat equation on the hyperbolic space: \begin{align}\label{abs:eqn} \left\{\begin{array}{ll} \partial_{t}u=Δ_{\mathbb{H…
On the critical mass Patlak-Keller-Segel system for multi-species populations: global existence and infinite time aggregation
Debabrata Karmakar, Gershon Wolansky
We study the global in time existence and long time asymptotics of solutions to the parabolic-elliptic Patlak-Keller-Segel system for the multi-species populations in the whole Euc…
On Patlak-Keller-Segel system for several populations: a gradient flow approach
Debabrata Karmakar, Gershon Wolansky
We study the global in time existence of solutions to the parabolic-elliptic Patlak-Keller-Segel system of multi-species populations. We prove that if the initial mass satisfies an…
Self-similar solutions of decaying Keller-Segel systems for several populations
Debabrata Karmakar, Gershon Wolansky
It is known that solutions of the parabolic elliptic Keller-Segel equations in the two dimensional plane decay, as time goes to infinity, provided the initial data admits sub-criti…