Dua Formula Eksponensial (Operator Linear dari Semigrup)

Assumed A is infinitesimal generator of C0-semigroup T(t) on X. This could be defined as T(t)=etA, applies if A is a bounded linear operator. Not if A is unbounded linear operator, then it will result in one possibility that show T(t) could be represented as etA. This paper will discuss and detail the proof of the other two formulas that show T(t) could be represented as etA.

A C0-Semigroup of Ulam Unstable Operators

The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t≥0 on C[0,1] such that for each t>0, Rt is Ulam unstable. Moreover, we compute the central moments of Rt and establish a Voronovskaja-type formula. This enables to prove that C2[0,1] is contained in the domain D(A) of the infinitesimal generator of the semigroup. We raise the problem to fully characterize the domain D(A).

Approximate controllability of random impulsive quasilinear evolution equation

In this paper, we study the approximate controllability of quasilinear evolution equation with random impulsive moments with less restriction and sufficient condition. The results are obtained by the theory of C0 semigroup of bounded linear operators on evolution equations.

Distributional Chaoticity of C0-Semigroup on a Frechet Space

This paper is mainly concerned with distributional chaos and the principal measure of C 0 -semigroups on a Frechet space. New definitions of strong irregular (semi-irregular) vectors are given. It is proved that if C 0 -semigroup T has strong irregular vectors, then T is distributional chaos in a sequence, and the principal measure μ p ( T ) is 1. Moreover, T is distributional chaos equivalent to that operator T t is distributional chaos for every ∀ t > 0 .

Fractional evolution equations with nonlocal conditions in partially ordered Banach space

In the present work, we discuss the existence of mild solutions for the initial value problem of fractional evolution equation of the form where C Dσ t denotes the Caputo fractional derivative of order σ ∈ (0, 1), −A : D(A) ⊂ X → X generates a positive C0-semigroup T(t)(t ≥ 0) of uniformly bounded linear operator in X, b > 0 is a constant, f is a given functions. For this, we use the concept of measure of noncompactness in partially ordered Banach spaces whose positive cone K is normal, and establish some basic fixed point results under the said concepts. In addition, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. We also supply some new coupled fixed point results via MNC. To justify the result, we prove an illustrative example that rational of the abstract results for fractional parabolic equations.