In this note we consider the nonlinear heat equation associated to the fractional Hermite operator Hβ= (- Δ + | x| 2) β, 0 < β≤ 1. We show the local solvability of the related Cauchy problem in the framework of modulation spaces. The result is obtained by combining tools from microlocal and time-frequency analysis. As a byproduct, we compute the Gabor matrix of pseudodifferential operators with symbols in the Hörmander class S^{0,0}_m, m∈ R.
On the local well-posedness of the nonlinear heat equation associated to the fractional Hermite operator in modulation spaces
Cordero E.
2021-01-01
Abstract
In this note we consider the nonlinear heat equation associated to the fractional Hermite operator Hβ= (- Δ + | x| 2) β, 0 < β≤ 1. We show the local solvability of the related Cauchy problem in the framework of modulation spaces. The result is obtained by combining tools from microlocal and time-frequency analysis. As a byproduct, we compute the Gabor matrix of pseudodifferential operators with symbols in the Hörmander class S^{0,0}_m, m∈ R.
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