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
Journal ISSN
Volume Title
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.
Rights
Attribution 4.0 International