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arXiv · 2610.08074

Confinement effects for semilinear fractional Hermite heat equations with nonlinearities of arbitrarily rapid growth

Divyang G. Bhimani·Mohamed Majdoub·Ramesh Manna
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Abstract

We study the Cauchy problem for a semilinear heat equation driven by the fractional harmonic oscillator. We establish local and global well-posedness in Orlicz and Morse--Transue spaces, based on sharp semigroup estimates and an integral compatibility condition between the Young function and the nonlinearity. We identify a critical Young function separating local well-posedness from instantaneous nonexistence for suitable data. Finally, we prove a confinement effect: under a Dini condition at the origin, small data yield global solutions decaying at the sharp exponential rate, with no Fujita-type restriction, in contrast with the corresponding free equation.

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Divyang G. Bhimani, Mohamed Majdoub, Ramesh Manna. 2026-10-06. Confinement effects for semilinear fractional Hermite heat equations with nonlinearities of arbitrarily rapid growth. https://arxiv.org/abs/2610.08074

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