An inhomogeneous nonlinear parabolic equation with concave nonlinearity

We establish both the existence and uniqueness of nonnegative global solutions for the nonlinear heat equation $u_{t} - Δ u = | x |^{- γ} u^{q}$ , $0 < q < 1$ , $γ > 0$ in the whole space $ℝ^{N}$ , and for nonnegative initial data $u_{0} \in C_{0} (ℝ^{N})$ .

PDF Access Denied

We have not been able to recognize your IP address 216.73.216.122 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

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

Mathematical Subject Classification

Primary: 35K05, 35K15

Secondary: 35A01, 35A02, 35D30, 35R05

Milestones

Received: 11 October 2024

Revised: 12 March 2025

Accepted: 27 March 2025

Published: 13 January 2026

Authors

Miguel Loayza
Departamento de Matemática Universidade Federal de Pernambuco Recife Brazil

Mohamed Majdoub
Department of Mathematics College of Science Imam Abdulrahman Bin Faisal University Dammam Saudi Arabia

Vol. 8, No. 1, 2026

Miguel Loayza and Mohamed Majdoub

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors