Nonexistence for parabolic differential inequalities with convection terms in exterior domains

2022/02/23 by Mohamed Jleli, Jleli, Mohamed, Bessem Samet +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.2202.11387

arxiv created 2022/02/23 · openalex publication_date 2022/02/23 · arxiv updated 2022/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are concerned with the nonexistence of sign-changing global weak solutions for a class of semilinear parabolic differential inequalities with convection terms in exterior domains. A weight function of the form t^α|x|^σ is considered in front of the power nonlinearity. Two types of non-homogeneous boundary conditions are investigated: Neumann-type and Dirichlet-type boundary conditions. Using a unified approach, for each case, we establish sufficient criteria for the nonexistence of global weak solutions. When α=0, the critical exponent in the sense of Fujita is obtained. This exponent is bigger than that found previously by Zheng and Wang (2008) in the case of homogeneous Neumann and Dirichlet boundary conditions.

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