6 papers
Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We consider the parabolic-elliptic Keller-Segel system in three dimensions and higher, corresponding to the mass supercritical case. We construct rigorously a solution which blows…
Refined description and stability for singular solutions of the 2D Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We construct solutions to the two dimensional parabolic-elliptic Keller-Segel model for chemotaxis that blow up in finite time . The solution is decomposed as the sum of a stati…
Spectral analysis for singularity formation of the two dimensional Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-sim…
Construction and Stability of type I blowup solutions for non-variational semilinear parabolic systems
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider in this note the semilinear heat system where the nonlinearity has no gradient structure taki…
Construction of type I blowup solutions for a higher order semilinear parabolic equation
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the higher-order semilinear parabolic equation in the whole space , where and is an odd…
Blowup solutions for a reaction-diffusion system with exponential nonlinearities
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the following parabolic system whose nonlinearity has no gradient structure: $$\left\{\begin{array}{ll} \partial_t u = Δu + e^{pv}, \quad & \partial_t v = μΔv + e^{qu},…