Asymptotic Properties of Solutions of the Fractional Diffusion-Wave Equation

2014/04/30 by Kochubei, Anatoly N. · 1 citation
#35K70 #35Q74 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 35R11. Secondary: 35B40

paper · doi:10.48550/arxiv.1404.7612

Abstract

For the fractional diffusion-wave equation with the Caputo-Dzhrbashyan fractional derivative of order α∈ (1,2) with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave equation and some other hyperbolic equations) and a pointwise stabilization property of solutions (similar to a well-known property of the heat equation and some other parabolic equations).

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