| Abstract: | The objective of this paper is to study a highly general model system of nonlinear equations that describe propagation of nerve impulses in a cell. We prove time-local existence of a classical solution, derive sufficient conditions for the existence of a time-global solution, and consider the question of eventual smoothing of discontinuous initial values. The large-time asymptotic expansion of the solutions of the Cauchy problem is constructed. The coefficients of the principal term of the asymptotic expression for the solution of the Cauchy problem are computed in terms of the Fourier transform of the initial values.The study has been partially supported by the Russian Foundation of Basic Research (93-011-131).Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 3, pp. 64–93, 1993. |
