The existence of a solution of the two-dimensional direct problem of propagation of the action potential along nerve fibers

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.