@article{Feng2025, 
author = {Tingfu Feng and Yan Dong and Kelei Zhang and Yan Zhu},
title = {Global existence and blow-up to coupled fourth-order parabolic systems arising from modeling epitaxial thin film growth},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {1},
pages = {263-289},
keywords = {blow-up, asymptotic behavior, global existence, epitaxial thin film growth, coupled fourth-order parabolic systems},
url = {https://www.sciopen.com/article/10.3934/cam.2025011},
doi = {10.3934/cam.2025011},
abstract = {This paper focuses on a class of fourth-order parabolic systems involving logarithmic and Rellich nonlinearities arising from modeling epitaxial thin film growth:         {                                                                                        u                  t                                            +                                                Δ                  2                                            u              =                                                                                          |                      v                      |                                                        p                                                                                                                        |                      u                      |                                                                            p                    −                    2                                                              u              ln              ⁡                              |                                  u                  v                                |                            −              μ                              u                                                                                                                              |                          x                          |                                                                    4                                                                                  ,                                                                                                            v                  t                                            +                                                Δ                  2                                            v              =                                                                                          |                      u                      |                                                        p                                                                                                                        |                      v                      |                                                                            p                    −                    2                                                              v              ln              ⁡                              |                                  u                  v                                |                            −              γ                              v                                                                                                                              |                          x                          |                                                                    4                                                                                            .                                  By using some new techniques to deal with the Rellich nonlinearities    μ      u                                                      |              x              |                                4                     and    γ      v                                                      |              x              |                                4                    , as well as the coupled logarithmic nonlinearities                      |        v        |            p                          |        u        |                    p        −        2              u  ln  ⁡      |          u      v        |   and                      |        u        |            p                          |        v        |                    p        −        2              v  ln  ⁡      |          u      v        |  , we prove the global existence and finite time blow-up of weak solutions. Furthermore, we not only obtain a new algebraic decay estimate and study the behavior of global weak solutions, but we also derive a new upper bound estimate for the blow-up time in case of the occurrence of blow-up.}
}