This paper deals with the construction of discrete numerical solutions of mixed problems for the telegraph equation. After discretization, the two-variables partial difference mixed problem is solved by means of a discrete eigenfunctions method that mimics the advantages of the continuous eigenfunction method while eliminating its computational disadvantages. The solution is based on a closed f...

The phenomenon of wave propagation failure in a discrete inhomogeneous Nagumo equation is investigated. It is found that the propagation failure occurs not only for small coupling coefficients but as well for an abrupt change of the interelement coupling. The investigation includes the study of the phase space of the system, numerical simulations, and real experiments with a nonlinear electrica...

We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a Fitzhugh-Nagumo type system.

The reaction-diffusion system of Fitzhugh Nagumo is considered. The initialboundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several dissipative models of viscoelasticity, biology, and superconductivity, some results on existence, uniqueness and a priori estimates are deduced both in the li...

In the present paper we derive the existence and uniqueness of a solution for the optimal control problem determined by a stochastic FitzHugh-Nagumo equation with recovery variable. In particular due the cubic non-linearity in the drift coefficients, standard techniques cannot be applied so that the Ekeland’s variational principle has to be exploited. AMS Classification subjects: 34K35, 35R60, ...

A periodic boundary value problem for nonlinear differential equation of the second order is studied. Nagumo condition is not assumed on a part of nonlinearity. Existence and multiplicity results are proved using the method of lower and upper solutions. Results are applied to the generalized Liénard oscillator.