Local behaviour of the solutions of the Chipot-Weissler equation

2023/03/14 by Marie-Françoise Bidaut-Véron, Bidaut-Véron, Marie-Françoise, Лаурент Верон +1 · 2 citations
Computer Science · Mathematics · #35B08 #35J62 #68D04 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Meromorphic and Entire Functions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2303.08074

openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the local properties of positive solutions of the equation -Δu=u^p-m|∇ u|^q in a punctured domain Ω∖\0\ of ℝ^N or in a exterior domain ℝ^N∖ B_r0 in the range min\p,q\>1 and m>0. We prove a series of a priori estimates depending p and q, and of the sign of q-\frac 2pp+1 and q-p. Using various techniques we obtain removability results for singular sets and we give a precise description of behaviour of solutions near an isolated singularity or at infinity in ℝ^N.

Cited by

• A dynamical system approach to the Chandrasekhar-Hamilton-Jacobi equation
• Singularities and asymptotics of solutions of the Chandrasekhar-Hailton-Jacobi equation

Related

• Isolated singularities of solutions of a 2-D diffusion equation with mixed reaction
• Singularities and asymptotics of solutions of the Chandrasekhar-Hailton-Jacobi equation
• Local and global properties of solutions of quasilinear Hamilton-Jacobi equations
• Isolated singularities of positive solutions of p-Laplacian type equations in R^d
• Regularizing effect of absorption terms in singular problems