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

@article{Souplet2015SinglepointBF,
title={Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities},
author={Philippe Souplet and Slim Tayachi},
journal={arXiv: Analysis of PDEs},
year={2015}
}
• Published 8 October 2015
• Mathematics
• arXiv: Analysis of PDEs
8 Citations
Construction and stability of type I blowup solutions for non-variational semilinear parabolic systems
• Mathematics
Advances in Pure and Applied Mathematics
• 2019
Abstract In this note, we consider the semilinear heat system ∂t⁡u=Δ⁢u+f⁢(v),∂t⁡v=μ⁢Δ⁢v+g⁢(u),μ>0,\partial_{t}u=\Delta u+f(v),\quad\partial_{t}v=\mu\Delta v+g(u),\quad\mu>0, where the nonlinearity
WELL-POSEDNESS, GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE HEAT EQUATION WITH GENERAL POWER-EXPONENTIAL NONLINEARITIES
• Mathematics
Proceedings of the International Congress of Mathematicians (ICM 2018)
• 2019
In this paper we consider the problem: $\partial_{t} u- \Delta u=f(u),\; u(0)=u_0\in \exp L^p(\R^N),$ where $p>1$ and $f : \R\to\R$ having an exponential growth at infinity with $f(0)=0.$ We prove
Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense
In this paper, we consider a numerical approach for fourth-order time fractional partial differential equation. This equation is obtained from the classical reaction-diffusion equation by replacing
Blowing Up Solutions for Nonlinear Parabolic Systems with Unequal Elliptic Operators
• Mathematics
Journal of Dynamics and Differential Equations
• 2019
We give sufficient conditions for the boundedness of the blow-up set and no boundary blow-up for type I blowing up solutions to a nonlinear parabolic system with unequal elliptic operators. We
Blow-up set of type I blowing up solutions for nonlinear parabolic systems
• Mathematics
• 2017
We consider the blow-up problem for systems of nonlinear parabolic inequalities and establish a criterion for the location of the blow-up set. Our criterion enables us to obtain sufficient conditions
Superlinear Parabolic Problems
• Mathematics
• 2019
Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.

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In this paper we study blowup of radially symmetric solutions of the nonlinear heat equation ut = Δu + |u|p−1u either on ℝN or on a finite ball under the Dirichlet boundary conditions. We assume that
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On considere le probleme aux valeurs limites et initiales: u t =Δu+f(u) dans Ω×(0,T), u(x,0)=Φ(x) si x∈Ω, u(x,t)=0 si x∈∂Ω, o<t<T, ou Ω est un domaine borne de R n a frontiere C 2