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Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems
Boumediene Abdellaoui, Somia Atmani, Kheireddine Biroud +1
In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, o…
Fractional elliptic reaction-diffusion systems with coupled gradient terms and different diffusion
Somia Atmani, Kheireddine Biroud, Maha Daoud +1
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of . The diffusion…
A class of fractional parabolic reaction-diffusion systems with control of total mass: theory and numerics
Maha Daoud, El-Haj Laamri, Azeddine Baalal
In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems posed in a bounded domain of . The…
Reaction-diffusion systems with initial data of low regularity
El-Haj Laamri, Benoît Perthame
Models issued from ecology, chemical reactions and several other application fields lead to semi-linear parabolic equations with super-linear growth. Even if, in general, blow-up c…
Existence of positive solutions to a nonlinear elliptic system with nonlinearity involving gradient term
Boumediene Abdellaoui, Ahmed Attar, El-Haj Laamri
In this work we analyze the existence of solutions to the nonlinear elliptic system: \begin{equation*} \left\{ \begin{array}{rcll} -Δu & = & v^q+\a g & \text{in }Ω, \\ -Δv& = &|\na…
Global Existence of classical solutions for a class of reaction-diffusion systems
El Haj Laamri
In this paper, we use duality arguments "à la Michel Pierre" to establish global existence of classic solutions for a class of parabolic reaction-diffusion systems modeling, for in…