Differential equations with fractional derivatives and their applications
Existence of positive and nodal solutions for local and nonlocal elliptic equations
| Full text | |
| Author(s): |
Zuo, Jiabin
;
Lopes, Juliana Honda
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 63, n. 6, p. 14-pg., 2022-06-01. |
| Abstract | |
In this work, we investigate the existence of local and global weak solutions for Kirchhoff-type diffusion problems driven by a magnetic fractional Laplacian (-delta)(A)(s) via the Galerkin method. Then, using the potential well method, we state some conditions on the initial energy, as in the case of the nonlocal Kirchhoff diffusion problem driven by fractional Laplacian, to ensure the existence of global in time solutions and blow-up in finite time solutions for our problem. The introduction of this problem could bring a new range of studies for this kind of diffusion problem. Published under an exclusive license by AIP Publishing (AU) | |
| FAPESP's process: | 20/14206-3 - Existence of weak solutions for a cell-fluid Navier-Stokes model with chemotaxis |
| Grantee: | Juliana Honda Lopes |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |