Boundedness and Regularity of Solutions for Nonlinear Parabolic Problem with two Singularities

Rabah Mecheter; Hichem Khelifi

doi:10.2478/tmmp-2025-0026

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Boundedness and Regularity of Solutions for Nonlinear Parabolic Problem with two Singularities

Tatra Mountains Mathematical Publications

Volume 90 (2025): Issue 2 (December 2025)

By: Rabah Mecheter and Hichem Khelifi

Open Access

|Dec 2025

Abstract

We examine the boundedness and regularity of weak solutions to a type of nonlinear parabolic equations with singular natural growth gradient terms. These equations also have a singular right-hand side with f ∈ L^m(Q_T ), (m ≥ 1). With suitable test functions, we can use Stampacchia’s lemma to prove that the solutions u(x, t) are bounded when $m > \frac{N}{p} + 1$ m > {N \over p} + 1 . Furthermore, we can establish a regularity result if f ∈ L¹(Q_T ).

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0026 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 123 - 148

Submitted on: Jan 27, 2025

Accepted on: Aug 21, 2025

Published on: Dec 18, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

regularity,

L^∞− solution,

nonlinear parabolic equations,

double singularities,

Related subjects:

© 2025 Rabah Mecheter, Hichem Khelifi, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 90 (2025): Issue 2 (December 2025)