Oscillatory and periodic solutions to a diffusion equation of neutral type

We examine a PDE with piecewise constant time delay. The equation is of neutral type since it contains the derivative u t at different values of the t ‐argument. Furthermore, the argument deviation changes its sign within intervals of unit length, so that the given PDE is alternately of retarded and advanced type. It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without delay. Of special interest is the appearance of periodic solutions as well as solutions asymptotically approaching closed curves which are not solutions of the equation studied.

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