RENORMALIZED AND ENTROPY SOLUTIONS TO THE GENERAL NONLINEAR PARABOLIC EQUATIONS IN MUSIELAK-ORLICZ SPACES

Ying Li; Chao Zhang

doi:10.1017/S1446788725101389

RENORMALIZED AND ENTROPY SOLUTIONS TO THE GENERAL NONLINEAR PARABOLIC EQUATIONS IN MUSIELAK-ORLICZ SPACES

Ying Li
, Chao Zhang^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents and double-phase growth.

Original language	English
Journal	Journal of the Australian Mathematical Society
DOIs	https://doi.org/10.1017/S1446788725101389
State	Accepted/In press - 2026
Externally published	Yes

Keywords

Entropy solutions
Existence
L1-data
Musielak-Orlicz spaces
Renormalized solutions
Uniqueness

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10.1017/S1446788725101389

Cite this

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title = "RENORMALIZED AND ENTROPY SOLUTIONS TO THE GENERAL NONLINEAR PARABOLIC EQUATIONS IN MUSIELAK-ORLICZ SPACES",

abstract = "We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents and double-phase growth.",

keywords = "Entropy solutions, Existence, L1-data, Musielak-Orlicz spaces, Renormalized solutions, Uniqueness",

author = "Ying Li and Chao Zhang",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2026. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.",

year = "2026",

doi = "10.1017/S1446788725101389",

language = "英语",

journal = "Journal of the Australian Mathematical Society",

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T1 - RENORMALIZED AND ENTROPY SOLUTIONS TO THE GENERAL NONLINEAR PARABOLIC EQUATIONS IN MUSIELAK-ORLICZ SPACES

AU - Li, Ying

AU - Zhang, Chao

N1 - Publisher Copyright: © The Author(s), 2026. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

PY - 2026

Y1 - 2026

N2 - We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents and double-phase growth.

AB - We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents and double-phase growth.

KW - Entropy solutions

KW - Existence

KW - L1-data

KW - Musielak-Orlicz spaces

KW - Renormalized solutions

KW - Uniqueness

UR - https://www.scopus.com/pages/publications/105028894809

U2 - 10.1017/S1446788725101389

DO - 10.1017/S1446788725101389

M3 - 文章

AN - SCOPUS:105028894809

SN - 1446-7887

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

ER -

RENORMALIZED AND ENTROPY SOLUTIONS TO THE GENERAL NONLINEAR PARABOLIC EQUATIONS IN MUSIELAK-ORLICZ SPACES

Abstract

Keywords

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