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New life-span results for the nonlinear heat equation
Slim Tayachi, Fred B. Weissler
We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation with initial values in Lebesgue, weighted Lebes…
Global existence and scattering for the inhomogeneous nonlinear Schrödinger equation
Lassaad Aloui, Slim Tayachi
In this paper we consider the inhomogeneous nonlinear Schrödinger equation $|K(x)|+|x|^s|\na…
Large time behavior of solutions to the nonlinear heat equation with absorption with highly singular antisymmetric initial values
Hattab Mouajria, Slim Tayachi, Fred B. Weissler
In this paper we study global well-posedness and long time asymptotic behavior of solutions to the nonlinear heat equation with absorption, , where $u=u(t,x)…
Global existence and decay estimates for the heat equation with exponential nonlinearity
Mohamed Majdoub, Slim Tayachi
In this paper we consider the initial value {problem } where and having an expon…
The nonlinear heat equation involving highly singular initial values and new blowup and life span results
Slim Tayachi, Fred B. Weissler
In this paper we prove local existence of solutions to the nonlinear heat equation $u_t = Δu +a |u|^αu, \; t\in(0,T),\; x=(x_1,\,\cdots,\, x_N)\in {\mathbb R}^N,\; a = \pm 1,\; α>0…
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: We const…