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- Title
NEW RESULTS ON CONTINUITY BY ORDER OF DERIVATIVE FOR CONFORMABLE PARABOLIC EQUATIONS.
- Authors
TUAN, NGUYEN HUY; NGUYEN, VAN TIEN; O'REGAN, DONAL; CAN, NGUYEN HUU; NGUYEN, VAN THINH
- Abstract
In this paper, we study the continuity problem by an order of derivative for conformable parabolic equations. The problem is examined in both the linear and nonlinear cases. For the input data in suitable Hilbert scale spaces, we consider the continuity problem for the linear problem. In the nonlinear case, we prove the existence of mild solutions for a class of conformable parabolic equations once the source function is a global Lipschitz type in the L s space sense. The main results are based on semigroup theory combined with the Banach fixed point theorem and Sobolev embeddings. We also inspect the continuity problem for the nonlinear model, and prove the convergence of the mild solution to the nonlinear problem as α tends to 1 − .
- Subjects
EMBEDDING theorems; NONLINEAR equations; EQUATIONS; CONTINUITY; HILBERT space
- Publication
Fractals, 2023, Vol 31, Issue 4, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X23400145