Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension Article Swipe

PDF

Ashish Bawalia , Zdzisław Brzeźniak , Manil T. Mohan ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2507.00160

We prove the global existence and the uniqueness of the $L^p\cap H_0^1-$valued ($2\leq p < \infty$) strong solutions of a nonlinear heat equation with constraints over bounded domains in any dimension $d\geq 1$. Along with the \textit{Faedo-Galerkin} approximation method and the compactness arguments, we utilize the monotonicity and the hemicontinuity properties of the nonlinear operators to establish the well-posedness results. In particular, we show that a Hilbertian manifold $\mathbb{M}$, which is the unit sphere in $L^2$ space, describing the constraint is invariant. Finally, in the asymptotic analysis, we generalize the recent work of [P. Antonelli, et. al. \emph{Calc. Var. Partial Differential Equations}, 63(4), 2024] to any bounded smooth domain in $\mathbb{R}^d$, $d\geq1$, when the corresponding nonlinearity is a damping. In particular, we show that, for positive initial datum and any $2\le p < \infty$, the unique positive strong solution of the above mentioned nonlinear heat equation with constraints converges in $L^p\cap H_0^1$ to the unique positive ground state.

Related Topics

Global Health

Global Network

Global Peace Index

Global Positioning System

Northrop Grumman Rq-4 Global Hawk

Paramount Global

Global City

Global Justice Movement

Bombardier Global Express

Global Justice

Global Airlines

Global North And Global South

Concepts

No concepts available.

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2507.00160
PDF: https://arxiv.org/pdf/2507.00160
OA Status: green
OpenAlex ID: https://openalex.org/W4416848241

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4416848241

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2507.00160

Digital Object Identifier
Title: Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2025

Year of publication
Publication date: 2025-06-30

Full publication date if available
Authors: Ashish Bawalia, Zdzisław Brzeźniak, Manil T. Mohan

List of authors in order
Landing page: https://arxiv.org/abs/2507.00160

Publisher landing page
PDF URL: https://arxiv.org/pdf/2507.00160

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2507.00160

Direct OA link when available
Cited by: 0

Total citation count in OpenAlex

Full payload

id	https://openalex.org/W4416848241
doi	https://doi.org/10.48550/arxiv.2507.00160
ids.doi	https://doi.org/10.48550/arxiv.2507.00160
ids.openalex	https://openalex.org/W4416848241
fwci
type	preprint
title	Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
is_xpac	False
apc_list
apc_paid
language	en
locations[0].id	pmh:oai:arXiv.org:2507.00160
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2507.00160
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2507.00160
locations[1].id	doi:10.48550/arxiv.2507.00160
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2507.00160
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5120529787
authorships[0].author.orcid
authorships[0].author.display_name	Ashish Bawalia
authorships[0].author_position	first
authorships[0].raw_author_name	Bawalia, Ashish
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5086680181
authorships[1].author.orcid	https://orcid.org/0000-0001-8731-6523
authorships[1].author.display_name	Zdzisław Brzeźniak
authorships[1].author_position	middle
authorships[1].raw_author_name	Brzeźniak, Zdzisław
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5046452698
authorships[2].author.orcid	https://orcid.org/0000-0003-3197-1136
authorships[2].author.display_name	Manil T. Mohan
authorships[2].author_position	last
authorships[2].raw_author_name	Mohan, Manil T.
authorships[2].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2507.00160
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension
has_fulltext	False
is_retracted	False
updated_date	2025-12-01T10:17:39.263697
primary_topic
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2507.00160
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2507.00160
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2507.00160
primary_location.id	pmh:oai:arXiv.org:2507.00160
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2507.00160
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2507.00160
publication_date	2025-06-30
publication_year	2025
referenced_works_count	0
abstract_inverted_index.a	19, 65, 117
abstract_inverted_index.p	13, 131
abstract_inverted_index.In	60, 119
abstract_inverted_index.We	0
abstract_inverted_index.in	28, 74, 83, 109, 149
abstract_inverted_index.is	70, 80, 116
abstract_inverted_index.of	8, 18, 51, 92, 139
abstract_inverted_index.to	55, 104, 152
abstract_inverted_index.we	43, 62, 87, 121
abstract_inverted_index.1$.	32
abstract_inverted_index.[P.	93
abstract_inverted_index.al.	96
abstract_inverted_index.and	5, 39, 47, 128
abstract_inverted_index.any	29, 105, 129
abstract_inverted_index.et.	95
abstract_inverted_index.for	124
abstract_inverted_index.the	2, 6, 9, 35, 40, 45, 48, 52, 57, 71, 78, 84, 89, 113, 134, 140, 153
abstract_inverted_index.<	14, 132
abstract_inverted_index.Var.	98
abstract_inverted_index.heat	21, 144
abstract_inverted_index.over	25
abstract_inverted_index.show	63, 122
abstract_inverted_index.that	64
abstract_inverted_index.unit	72
abstract_inverted_index.when	112
abstract_inverted_index.with	23, 34, 146
abstract_inverted_index.work	91
abstract_inverted_index.$2\le	130
abstract_inverted_index.$L^2$	75
abstract_inverted_index.2024]	103
abstract_inverted_index.Along	33
abstract_inverted_index.above	141
abstract_inverted_index.datum	127
abstract_inverted_index.prove	1
abstract_inverted_index.that,	123
abstract_inverted_index.which	69
abstract_inverted_index.$d\geq	31
abstract_inverted_index.63(4),	102
abstract_inverted_index.H_0^1$	151
abstract_inverted_index.domain	108
abstract_inverted_index.global	3
abstract_inverted_index.ground	156
abstract_inverted_index.method	38
abstract_inverted_index.recent	90
abstract_inverted_index.smooth	107
abstract_inverted_index.space,	76
abstract_inverted_index.sphere	73
abstract_inverted_index.state.	157
abstract_inverted_index.strong	16, 137
abstract_inverted_index.unique	135, 154
abstract_inverted_index.($2\leq	12
abstract_inverted_index.Partial	99
abstract_inverted_index.bounded	26, 106
abstract_inverted_index.domains	27
abstract_inverted_index.initial	126
abstract_inverted_index.utilize	44
abstract_inverted_index.$L^p\cap	10, 150
abstract_inverted_index.Finally,	82
abstract_inverted_index.\infty$)	15
abstract_inverted_index.\infty$,	133
abstract_inverted_index.damping.	118
abstract_inverted_index.equation	22, 145
abstract_inverted_index.manifold	67
abstract_inverted_index.positive	125, 136, 155
abstract_inverted_index.results.	59
abstract_inverted_index.solution	138
abstract_inverted_index.$d\geq1$,	111
abstract_inverted_index.analysis,	86
abstract_inverted_index.converges	148
abstract_inverted_index.dimension	30
abstract_inverted_index.establish	56
abstract_inverted_index.existence	4
abstract_inverted_index.mentioned	142
abstract_inverted_index.nonlinear	20, 53, 143
abstract_inverted_index.operators	54
abstract_inverted_index.solutions	17
abstract_inverted_index.Antonelli,	94
abstract_inverted_index.Hilbertian	66
abstract_inverted_index.arguments,	42
abstract_inverted_index.asymptotic	85
abstract_inverted_index.constraint	79
abstract_inverted_index.describing	77
abstract_inverted_index.generalize	88
abstract_inverted_index.invariant.	81
abstract_inverted_index.properties	50
abstract_inverted_index.uniqueness	7
abstract_inverted_index.Equations},	101
abstract_inverted_index.\emph{Calc.	97
abstract_inverted_index.compactness	41
abstract_inverted_index.constraints	24, 147
abstract_inverted_index.particular,	61, 120
abstract_inverted_index.Differential	100
abstract_inverted_index.monotonicity	46
abstract_inverted_index.nonlinearity	115
abstract_inverted_index.$\mathbb{M}$,	68
abstract_inverted_index.H_0^1-$valued	11
abstract_inverted_index.approximation	37
abstract_inverted_index.corresponding	114
abstract_inverted_index.hemicontinuity	49
abstract_inverted_index.well-posedness	58
abstract_inverted_index.$\mathbb{R}^d$,	110
abstract_inverted_index.\textit{Faedo-Galerkin}	36
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile