An inhomogeneous nonlinear parabolic equation with concave nonlinearity

Miguel Loayza; Mohamed Majdoub

doi:10.2140/tunis.2026.8.41

An inhomogeneous nonlinear parabolic equation with concave nonlinearity

Miguel Loayza
, Mohamed Majdoub

Mathematics Department

Universidade Federal de Pernambuco

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

Abstract

We establish both the existence and uniqueness of nonnegative global solutions for the nonlinear heat equation (Formula presented) in the whole space R^N, and for nonnegative initial data u₀ 2 C₀.R^N/.

Original language	English
Pages (from-to)	41-58
Number of pages	18
Journal	Tunisian Journal of Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.2140/tunis.2026.8.41
State	Published - Jan 2026

Keywords

inhomogeneous concave nonlinearity
local existence
nonlinear heat equation
singular data
uniqueness

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10.2140/tunis.2026.8.41

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title = "An inhomogeneous nonlinear parabolic equation with concave nonlinearity",

abstract = "We establish both the existence and uniqueness of nonnegative global solutions for the nonlinear heat equation (Formula presented) in the whole space RN, and for nonnegative initial data u0 2 C0.RN/.",

keywords = "inhomogeneous concave nonlinearity, local existence, nonlinear heat equation, singular data, uniqueness",

author = "Miguel Loayza and Mohamed Majdoub",

note = "Publisher Copyright: {\textcopyright} 2026 MSP (Mathematical Sciences Publishers).",

year = "2026",

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doi = "10.2140/tunis.2026.8.41",

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AU - Majdoub, Mohamed

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AB - We establish both the existence and uniqueness of nonnegative global solutions for the nonlinear heat equation (Formula presented) in the whole space RN, and for nonnegative initial data u0 2 C0.RN/.

KW - inhomogeneous concave nonlinearity

KW - local existence

KW - nonlinear heat equation

KW - singular data

KW - uniqueness

UR - https://www.scopus.com/pages/publications/105034415535

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DO - 10.2140/tunis.2026.8.41

M3 - Article

AN - SCOPUS:105034415535

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VL - 8

SP - 41

EP - 58

JO - Tunisian Journal of Mathematics

JF - Tunisian Journal of Mathematics

IS - 1

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An inhomogeneous nonlinear parabolic equation with concave nonlinearity

Abstract

Keywords

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