Inhomogeneous Two-Parameter Abstract Cauchy Problem

inhomogeneous two-parameter abstract cauchy problem

A Two-parameter Generalized Skew-Cauchy Distribution

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC(&lambda1, &lambda2), that it has more flexible than the skew-Cauchy distribution (denoted by SC(&lambda)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC(&lambd...

A singular abstract cauchy problem.

In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

Inhomogeneous Gevrey Ultradistributions and Cauchy Problem

AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.

The Cauchy problem for the inhomogeneous porous medium equation

We consider the initial value problem for the filtration equation in an inhomogeneous medium ρ(x)ut = ∆u, m > 1. The equation is posed in the whole space R, n ≥ 2, for 0 < t < ∞ ; ρ(x) is a positive and bounded function with a certain behaviour at infinity. We take initial data u(x, 0) = u0(x) ≥ 0, and prove that this problem is well-posed in the class of solutions with finite “energy”, that is...

Factoring Weakly Compact Operators and the Inhomogeneous Cauchy Problem

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.