An inhomogeneous nonlinear parabolic equation with concave nonlinearity

2023/11/29 by Loayza, Miguel, Majdoub, Mohamed
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.17579

Abstract

We establish both the existence and uniqueness of non-negative global solutions for the nonlinear heat equation u_t-Δu=|x|^-γ u^q, 00 in the whole space ℝ^N, and for non-negative initial data u₀∈ C₀(ℝ^N).

Related

• Existence and non-existence of global solutions for a heat equation with degenerate coefficients
• Parabolic equations with concave non-linearity
• Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up
• Critical exponent for the global existence of solutions to a nonlinear degenerate/singular parabolic equation
• Global existence and blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition