A strange non-local monotone operator arising in the homogenization of a diffusion equation with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape
| dc.contributor.author | Diaz, Jesus Ildefonso | |
| dc.contributor.author | Shaposnikova, Tatiana | |
| dc.contributor.author | Zubova, Maria | |
| dc.date.accessioned | 2023-04-25T15:52:13Z | |
| dc.date.available | 2023-04-25T15:52:13Z | |
| dc.date.issued | 2022-07-18 | |
| dc.description.abstract | We characterize the homogenization limit of the solution of a Poisson equation in a bounded domain, either periodically perforated or containing a set of asymmetric periodical small particles and on the boundaries of these particles a nonlinear dynamic boundary condition holds involving a Hölder nonlinear σ(u). We consider the case in which the diameter of the perforations (or the diameter of particles) is critical in terms of the period of the structure. As in many other cases concerning critical size, a "strange" nonlinear term arises in the homogenized equation. For this case of asymmetric critical particles we prove that the effective equation is a semilinear elliptic equation in which the time arises as a parameter and the nonlinear expression is given in terms of a nonlocal operator H which is monotone and Lipschitz continuous on L2(0,T), independently of the regularity of σ. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 32 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Díaz, J. I., Shaposhnikova, T. A., & Zubova, M. N. (2022). A strange non-local monotone operator arising in the homogenization of a diffusion equation with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape. <i>Electronic Journal of Differential Equations, 2022</i>(52), pp. 1-32. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16642 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Critically scaled homogenization | |
| dc.subject | Asymmetric particles | |
| dc.subject | Dynamic boundary conditions | |
| dc.subject | Hölder continuous reactions | |
| dc.subject | Strange term | |
| dc.subject | Nonlocal monotone operator | |
| dc.title | A strange non-local monotone operator arising in the homogenization of a diffusion equation with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape | |
| dc.type | Article |