S. Tayachi

activity

20132026

most citedLocal well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity

6 citations · 12 across the 15 of their papers we have counts for

collaborators

Showing 2015Show all

3 papers · 1 filter

math.AP2015

Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities

Philippe Souplet, Slim Tayachi

We study positive blowing-up solutions of systems of the form: $u_{t} = δ_{1} Δ u + e^{p v}, v_{t} = δ_{2} Δ v + e^{q u},$ with $δ_{1}, δ_{2} > 0$ and $p, q > 0$ . We prove single-point blow-up for large…

math.AP2015

Existence of a Stable Blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term

Slim Tayachi, Hatem Zaag

We consider the nonlinear heat equation with a nonlinear gradient term: $\partial_{t} u = Δ u + μ ∣\nabla u ∣^{q} + ∣ u ∣^{p - 1} u, μ > 0, q = 2 p / (p + 1), p > 3, t \in (0, T), x \in R^{N} .$ We const…

math.AP2015

Improved conditions for single-point blow-up in reaction-diffusion systems

Nejib Mahmoudi, Philippe Souplet, Slim Tayachi

We study positive blowing-up solutions of the system: $u_{t} - δ Δ u = v^{p}, v_{t} - Δ v = u^{q},$ as well as of some more general systems. For any $p, q > 1$ , we prove single-point blo…