On Coercive Solvability of Parabolic Equations with Variable Operators

In a Banach space E, the Cauchy problem υ′(t)+A(t)υ(t)=f(t)(0≤t≤1),υ(0)=υ0, is considered for a differential equation with linear strongly positive operator A(t) such that its domain D = D(A(t)) does not depend on t and is everywhere dense in E and A(t) generates an analytic semigroup exp{−sA(t)}(s ≥ 0). Under natural assumptions on A(t), we prove the coercive solvability of the Cauchy problem in the Banach space C0β,γ (E). We prove a stronger estimate for the solution compared with estimates known earlier, using weaker restrictions on f(t) and v 0 . © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Authors
Publisher
Springer New York LLC
Number of issue
5
Language
English
Pages
706-724
Status
Published
Volume
239
Year
2019
Organizations
  • 1 RUDN University, Moscow, Russian Federation
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38584/