We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call this a subspace of stability. For more ge...

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by Nigmatullin (1986), and Zaslavsky (1994) in R for modeling some physical phenomena. The fractional derivative models time delays in a diffusion process. We will give a survey of the recent results on the fractional Cauchy problem and its generalizati...

The notion of invariance under transformations (changes of coordinates) of the Cauchy mean-value expression is introduced and then used in furnishing a suitable two-variable version of a result by L. Losonczi on equality of many-variable Cauchy means. An assessment of the methods used by Losonczi and Matkowski is made and an alternative way is proposed to solve the problem of representation of ...

We review some results about the computational power of several computational models. Considered models have in common to be related to continuous dynamical systems. 1 Dynamical Systems and Polynomial Cauchy Problems A polynomial Cauchy problem is a Cauchy problem of type { x′ = p(x, t) x(0) = x0 where p(x, t) is a vector of polynomials, and x0 is some initial condition. The class of functions ...