Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.08074

Authors: Bhimani, Divyang G., Majdoub, Mohamed, Manna, Ramesh

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Arthritis National Research Foundation, Imam Abdulrahman Bin Faisal University

OpenAlex ID: W7221041423

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