Abstract
A class of non-local problems, Dtρu(t) + Au(t) = f(t) (1 < ρ < 2, 0 < t ≤ T), αu(0) + βu(ξ) = ’; u0(0) = (α; β are constants and ξ 2 (0; T) is a fixed number), in an arbitrary separable Hilbert space H is considered. Here A is a strongly positive selfadjoint operator with the domain of definition D(A) and Dtρ is the Caputo derivative. The main goal of the work is to study the correctness of the problem depending on the pair of parameters (α; β) 2 R2. If jαj > jβj and ’; 2 D(A), then the solution of the problem exists and is unique. Inequalities of coercivity type are obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
