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Research Article | Open Access

Uniformly analytic solutions to a class of singular partial differential equations

John Paolo O. Soto, Jose Ernie C. Lope, Mark Philip F. Ona( )
Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia Avenue, U.P. Campus, Diliman, Quezon City 1001, Philippines
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Abstract

We study the singular nonlinear partial differential equation t ∂ t u = F ( t , x , u , ∂ x u ), where ( t , x ) ∈ R × R n . Under some growth conditions on the coefficients of the partial Taylor expansion of F, we construct the unique solution that is continuous in t and C ∞ in x.

Keywords

uniformly analytic functionssingular partial differential equation
CLC number: 35A01, 35A02, 35F20

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10400-10421
DOI: 10.3934/math.2022580

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Cite this article:
Soto JPO, Lope JEC, Ona MPF. Uniformly analytic solutions to a class of singular partial differential equations. AIMS Mathematics, 2022, 7(6): 10400-10421. https://doi.org/10.3934/math.2022580

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Received: 10 October 2021
Revised: 21 March 2022
Accepted: 22 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)