A dynamical system approach to the Chandrasekhar-Hamilton-Jacobi equation

2025/06/25 by Bidaut-Véron, Marie-Françoise, Véron, Laurent
#35J62 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.07110

Abstract

We study the local properties of positive solutions of the equation -Delta u= exp(u) in a punctured domain Omega of RN in the range of parameters q > 1 and M > 0. We prove a series of a priori estimates near a singular point. In the case of radial solutions we use various techniques inherited from the dynamical systems theory to obtain the precise behaviour of singular solutions. We prove also the existence of singular solutions with these precise behaviours.

Citations

• Singularities and asymptotics of solutions of the Chandrasekhar-Hailton-Jacobi equation
• Isolated singularities of solutions of a 2-D diffusion equation with mixed reaction
• Local behaviour of the solutions of the Chipot-Weissler equation
• Singular solutions of some elliptic equations involving mixed absorption-reaction
• Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

Related

• Singularities and asymptotics of solutions of the Chandrasekhar-Hailton-Jacobi equation
• Singularities of solutions of Hamilton-Jacobi equations
• Isolated initial singularities for the viscous Hamilton-Jacobi equation
• A perturbation problem involving singular perturbations of domains for Hamilton-Jacobi equations
• Local and global properties of solutions of quasilinear Hamilton-Jacobi equations