Alternative Infinitesimal Generator of Invertible Evolution Families

نویسنده

  • Yoritaka Iwata
چکیده

A logarithm representation of evolution operators is defined. Generators of invertible evolution families are characterized by the logarithm representation. In this article, using the logarithm representation, a concept of evolution operators without satisfying the semigroup property is introduced. In conclusion the existence of alternative infinitesimal generator is clarified.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Existence and Uniqueness of Mild and Classical Solutions of Impulsive Evolution Equations

We consider the non-linear impulsive evolution equation u′(t) = Au(t) + f(t, u(t), Tu(t), Su(t)), 0 < t < T0, t 6= ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, 3, . . . , p. in a Banach space X, where A is the infinitesimal generator of a C0 semigroup. We study the existence and uniqueness of the mild solutions of the evolution equation by using semigroup theory and then show that the mild solu...

متن کامل

A Power Matrix Approach to the Witt Algebra and Loewner Equations

The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of power matrices, and the coefficients are entire functions of finitely many coefficients of the infinitesimal generator. Furthermore coefficients of the solution...

متن کامل

Viability of a Time Dependent Closed Set with Respect to a Semilinear Delay Evolution

We prove a sufficient condition for a time-dependent closed set to be viable with respect to a delay evolution inclusion governed by a strongly-weakly u.s.c. perturbation of an infinitesimal generator of a C0-semigroup. This condition is expressed in terms of a natural concept involving tangent sets, generalizing tangent vectors in the sense of Bouligand and Severi. Mathematics Subject Classifi...

متن کامل

The Black-Scholes Equation and its Relation with Semigroups of Operators

This paper gives a connection between the theory of semigroups of operators (functional analysis) and mathematical finance through the Black-Scholes equation. Besides using this theory obtain the solution of this equation via the infinitesimal generator of a group of evolution. Mathematics Subject Classification: Primary 91G80; Secondary 47D06

متن کامل

A Class of Nonlinear Evolution Equations in a Banach Space

where the unknown function/is from a real number interval into a Banach space X. For suitable real numbers t and vectors x in X, Ait, x) is the infinitesimal generator of a holomorphic semigroup of linear contraction operators in X, and certain regularity requirements are placed on the function (/, x) -> Ait, x). After proving a local existence, uniqueness, and stability theorem for (*), we con...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017