Open AccessThe existence of a solution of the two-dimensional direct problem of propagation of the action potential along nerve fibers
Author(s) -
A.J. Satybaev,
G.S. Kurmanalieva
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1905287s
Subject(s) - mathematics , laplace transform , action (physics) , equivalence (formal languages) , piecewise , mathematical analysis , gravitational singularity , function (biology) , pure mathematics , physics , quantum mechanics , evolutionary biology , biology
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.