This paper examines finite-time stability of homogeneous systems. The main result is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity.

In this work, we will prove the Hyers–Ulam stability of linear partial differential equations of first order.

We prove that an independent system of equations in three variables with a nonperiodic solution and at least two equations consists of balanced equations only. For that, we show that the intersection of two different entire systems contains only balanced equations, where an entire system is the set of all equations solved by a given morphism. Furthermore, we establish that two equations which h...

1.1 Fix a variety X over C. The Riemann-Hilbert correspondence identifies the category of perverse sheaves on X(C) with the (abelian) category of regular holonomic D-modules on X. This is a remarkable and deep theorem in the theory of linear partial differential equations. In this note we will investigate this correspondence in simple examples, exploring the topological and algebraic sides as w...

The 14 moments model for dense gases, introduced in the last few years by Arima, Taniguchi, Ruggeri and Sugiyama, is here extended up to 18 moments. They have found the closure of the balance equations up to a finite order with respect to equilibrium; it is also possible to impose for that model the entropy and Galilean relativity principles up to whatever order with respect to equilibrium, but...

The π-derivative for fuzzy function is considered. Consequently, using this π-derivative we study fuzzy differentuial equations. In particular, we build a solution for a fuzzy differential equation with the help of a system of ordinary differential equations which is generates of the π-derivative. Keywords— π-derivative for set valued functions, derivative for fuzzy functions, fuzzy differentia...

Xu (2004), Kolm (2004; 2009) and Miyagishima (2009) study the problem of ranking linear budget sets in terms of freedom of choice. In their researches, the set of available goods is fixed. However, there would be cases in which new goods become available due to innovation. Recent examples of such goods include commodities and services relevant to information technology. In this paper, we consid...

A new method for solving boundary value problems has been recently introduced by the author [1]. The implementation of this method to linear elliptic PDEs in two space variables is discussed in [2–4]. Here we concentrate on evolution equations in one and two space variables, which will be denoted by x and by (x1, x2) respectively. We assume that the space variables are on the half line. The cas...