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Main Authors:	Bhimani, Divyang G., Majdoub, Mohamed, Manna, Ramesh
Format:	Preprint
Published:	2023
Subjects:	Analysis of PDEs Functional Analysis
Online Access:	https://arxiv.org/abs/2306.02828
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author	Bhimani, Divyang G. Majdoub, Mohamed Manna, Ramesh
author_facet	Bhimani, Divyang G. Majdoub, Mohamed Manna, Ramesh
contents	We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity. We establish local well-posedness within the appropriate Orlicz spaces. Through the examination of small initial data in suitable Orlicz spaces, we obtain the existence of global weak-mild solutions. Additionally, precise decay estimates are presented for large time, indicating that the decay rate is influenced by the nonlinearity's behavior near the origin. Moreover, we highlight that the existence of local nonnegative classical solutions is no longer guaranteed when certain nonnegative initial data is considered within the appropriate Orlicz space.
format	Preprint
id	arxiv_https___arxiv_org_abs_2306_02828
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	Heat equations associated to harmonic oscillator with exponential nonlinearity Bhimani, Divyang G. Majdoub, Mohamed Manna, Ramesh Analysis of PDEs Functional Analysis We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity. We establish local well-posedness within the appropriate Orlicz spaces. Through the examination of small initial data in suitable Orlicz spaces, we obtain the existence of global weak-mild solutions. Additionally, precise decay estimates are presented for large time, indicating that the decay rate is influenced by the nonlinearity's behavior near the origin. Moreover, we highlight that the existence of local nonnegative classical solutions is no longer guaranteed when certain nonnegative initial data is considered within the appropriate Orlicz space.
title	Heat equations associated to harmonic oscillator with exponential nonlinearity
topic	Analysis of PDEs Functional Analysis
url	https://arxiv.org/abs/2306.02828

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