Existence and uniqueness of the p-generalized modified error function

Date

2020-04-18

Authors

Bollati, Julieta
Semitiel, Jose A.
Natale, Maria F.
Tarzia, Domingo A.

Journal Title

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Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x = 0. We prove existence and uniqueness of a non-negative C∞ solution by using a fixed point argument. We show that the p-generalized modified error function converges to the p-Dirichlet boundary condition. In both problems, for p = 1, the generalized modified error function and the modified error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition.

Description

Keywords

Modified error function, Generalized modified error function, Nonlinear ordinary differential equation, Banach fixed point theorem, Stefan problem

Citation

Bollati, J., Semitiel, J. A., Natale, M. F., & Tarzia, D. A. (2020). Existence and uniqueness of the p-generalized modified error function. <i>Electronic Journal of Differential Equations, 2020</i>(35), pp. 1-11.

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Attribution 4.0 International

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