62 citations · 261 across the 45 of their papers we have counts for
7 papers · 2 filters
A modulation technique for the blow-up profile of the vector-valued semilinear wave equation
Asma Azaiez, Hatem Zaag
We consider a vector-valued blow-up solution with values in for the semilinear wave equation with power nonlinearity in one space dimension (this is a system of PDEs…
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: $$\partial_t U = ΔU + α|\nabla U|^2 + e^U,\quad (x, t)\in\mathbb{R}^N\times[0…
Construction and stability of blowup solutions for a non-variational semilinear parabolic system
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the following parabolic system whose nonlinearity has no gradient structure: $$\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+…
Existence and stability of a blow-up solution with a new prescribed behavior for a heat equation with a critical nonlinear gradient term
Slim Tayachi, Hatem Zaag
We consider the semilinear heat equation, to which we add a nonlinear gradient term, with a critical power. We construct a solution which blows up in finite time. We also give a sh…
Blow-up solutions to the semilinear wave equation with a stylized pyramid as a blow-up surface
Frank Merle, Hatem Zaag
We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic b…