21 citations · 75 across the 13 of their papers we have counts for
18 papers
Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
It is well-known that the two-dimensional parabolic-elliptic Keller-Segel system admits finite-time blowup solutions, which is the case if the initial density has total mass greate…
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: $$\left\{\begin{array}{ll} \partial_t u = Δu + e^{pv}, \quad & \partial_t v = μΔv + e^{qu},…
Construction of a stable blowup solution with a prescribed behavior for a non-scaling invariant semilinear heat equation
G. K. Duong, V. T. Nguyen, H. Zaag
We consider the semilinear heat equation \begin{eqnarray*} \partial_t u = Δu + |u|^{p-1} u \ln ^α( u^2 +2), \end{eqnarray*} in the whole space , where and $ α…
Construction of type II blowup solutions for the 1-corotational energy supercritical wave maps
Tej-Eddine Ghoul, Slim Ibrahim, Van Tien Nguyen
We consider the energy supercritical wave maps from into the -sphere with . Under an additional assumption of 1-corotational symmetry, th…
Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the following exponential reaction-diffusion equation involving a nonlinear gradient term: $$\partial_t U = ΔU + α|\nabla U|^2 + e^U,\quad (x, t)\in\mathbb{R}^N\times[0…
On the stability of type II blowup for the 1-corotational energy supercritical harmonic heat flow
Tej-Eddine Ghoul, Slim Ibrahim, Van Tien Nguyen
We consider the energy supercritical harmonic heat flow from into the -sphere with . Under an additional assumption of 1-corotational sym…
Construction and stability of blowup solutions for a non-variational semilinear parabolic system
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 + |v|^{p-1}v, \quad & \partial_t v = μΔv + |u|…
Refined regularity of the blow-up set linked to refined asymptotic behavior for the semilinear heat equation
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider , a solution of which blows up at some time , where , and $(N-2)p < N+…
Finite degrees of freedom for the refined blow-up profile of the semilinear heat equation
Van Tien Nguyen, Hatem Zaag
We refine the asymptotic behavior of solutions to the semilinear heat equation with Sobolev subcritical power nonlinearity which blow up in some finite time at a blow-up point wher…
Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method
Van Tien Nguyen, Hatem Zaag
We consider a blow-up solution for a strongly perturbed semilinear heat equation with Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we f…
Construction of a stable blow-up solution for a class of strongly perturbed semilinear heat equations
Van Tien Nguyen, Hatem Zaag
We construct a solution for a class of strongly perturbed semilinear heat equations which blows up in finite time with a prescribed blow-up profile. The construction relies on the…
On the blow-up results for a class of strongly perturbed semilinear heat equations
Van Tien Nguyen
We consider in this work some class of strongly perturbed for the semilinear heat equation with Sobolev sub-critical power nonlinearity. We first derive a Lyapunov functional in si…
Numerical analysis of the rescaling method for parabolic problems with blow-up in finite time
Van Tien Nguyen
In this work, we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the…