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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bhimani2026confinement,
  title = {{Confinement effects for semilinear fractional Hermite heat equations with nonlinearities of arbitrarily rapid growth}},
  author = {Divyang G. Bhimani and Mohamed Majdoub and Ramesh Manna},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08074},
  eprint = {2610.08074},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08074},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Confinement effects for semilinear fractional Hermite heat equations with nonlinearities of arbitrarily rapid growth
AU  - Divyang G. Bhimani
AU  - Mohamed Majdoub
AU  - Ramesh Manna
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08074
UR  - https://arxiv.org/abs/2610.08074
AB  - 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.
ER  -