Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation

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...

Inhomogeneous Two-Parameter Abstract Cauchy Problem

On the Superstability and Stability of the Pexiderized Exponential Equation

The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $S$ to an arbitrary unitary complex Banachalgebra and also $psi: S^{2}rightarrow [0,infty)$ is afunction. Fur...

inhomogeneous two-parameter abstract cauchy problem

Inhomogeneous Gevrey Ultradistributions and Cauchy Problem

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