The existence of a solution of the two-dimensional direct problem of propagation of the action potential along nerve fibers
Year: 2019
Type: article
Abstract: In this article, we consider a generalized parabolic two-dimensional direct problem of the process of propagation of the action potential along nerve fibers. The problem is reduced to a generalized hyperbolic problem using the Laplace transform. A generalized two-dimensional direct hyperbolic problem is reduced to a regular hyperbolic problem using methods for rectifying characteristics and isolating singularities. Using the piecewise-continuous function, the existence of the solution of the last problem is proved. From the equivalence of problems it follows that there exists a generalized solution of the parabolic problem.
Source: Filomat
DOI: 10.2298/fil1905287s
Authors: A.J. Satybaev, G.S. Kurmanalieva
Institution: Osh Technological University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3000326526