Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation

2024/08/02 by Leandro M. Del Pezzo, Del Pezzo, L., Rodrigo José Pires Ferreira +1 · 3 citations
Mathematics · Engineering · #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2408.01577

Abstract

In this paper we consider the blow-up problem for a mixed local-nonlocal diffusion operator, u_t=aΔu -b(-Δ)^s u+u^p. We show that the Fujita exponent is given by the nonlocal part, p_F=1+2s/N. We also determinate, in some cases, the blow-up rate.

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• Sharp behavior of semilinear damped wave equations driven by mixed local-nonlocal operators
• Blow-up criteria for the semilinear parabolic equations driven by mixed local-nonlocal operators
• Blow-up for a Nonlocal Diffusion Equation with Time Regularly Varying Nonlinearity and Forcing

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