Final value problem for parabolic equation with fractional Laplacian and Kirchhoff's term
Summary: 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 \(\delta\) tends to zero.
global existence and uniqueness of mild solutions
scientific article; zbMATH DE number 7393912
scientific article