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Journal of Mathematical Sciences

, Volume 239, Issue 5, pp 706–724 | Cite as

On Coercive Solvability of Parabolic Equations with Variable Operators

  • A. R. HanalyevEmail author
Article

Abstract

In a Banach space E, the Cauchy problem

$$ \upsilon^{\prime }(t)+A(t)\upsilon (t)=f(t)\kern1em \left(0\le t\le 1\right),\kern1em \upsilon (0)={\upsilon}_0, $$

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 \( {C}_0^{\beta, \upgamma} \) (E). We prove a stronger estimate for the solution compared with estimates known earlier, using weaker restrictions on f(t) and v0.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.RUDN UniversityMoscowRussia

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