COERCIVE SOLVABILITY OF PARABOLIC DIFFERENTIAL EQUATIONS WITH DEPENDENT OPERATORS

COERCIVE SOLVABILITY OF PARABOLIC DIFFERENTIAL EQUATIONS WITH DEPENDENT OPERATORS

A. Ashyralyev, A. Hanalyev

[PDF]

Abstract

In the present paper the nonlocal-boundary value problem for the differential equation of parabolic type

v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T

in an arbitrary Banach space with the linear positive operators A(t) is considered. The well-posedness of this problem is established in Banach space C^{β, γ}₀(E) of all continuous functions E-valued functions φ(t) on [0, T] satisfying a H�lder condition with a weight(t+τ)^γ. New exact estimates in Holder norms for the solution of three nonlocal-boundary value problems for parabolic equations are obtained.

Keywords

Parabolic equations, NBV problems, Banach spaces, positive operators.