Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff's Term. (3rd July 2021)

• Record Type: Journal Article
• Authors: Luc, Nguyen Hoang; Kumar, Devendra; Long, Le Dinh; Van, Ho Thi Kim
• Other Names: Kumar Santosh Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-07-03
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/7238678
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived. The main tools for analysis in this paper are the Banach fixed point theory and Sobolev embeddings. In addition, to investigate the regularity, we also further study the nonwell-posed and give the regularized methods to get the correct approximate solution. With reasonable and appropriate input conditions, we can prove that the error between the regularized solution and the search solution is towards zero when δ tends to zero.