Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent
We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-03-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2022-0306 |
| _version_ | 1797848784583000064 |
|---|---|
| author | Deng Yanhua Tan Zhong Xie Minghong |
| author_facet | Deng Yanhua Tan Zhong Xie Minghong |
| author_sort | Deng Yanhua |
| collection | DOAJ |
| description | We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity. |
| first_indexed | 2024-04-09T18:33:01Z |
| format | Article |
| id | doaj.art-65d961a712e14a69a96b90294c4f911c |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-04-09T18:33:01Z |
| publishDate | 2023-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-65d961a712e14a69a96b90294c4f911c2023-04-11T17:07:12ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2023-03-011212100212410.1515/anona-2022-0306Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponentDeng Yanhua0Tan Zhong1Xie Minghong2School of Mathematical Sciences, Xiamen Institute of Technology, Xiamen 361005, ChinaSchool of Mathematical Science and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, ChinaSchool of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, ChinaWe consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity.https://doi.org/10.1515/anona-2022-0306dirichlet-to-neumann operatorcritical exponentblowupconcentration phenomenon35k5535b3335b4035b44 |
| spellingShingle | Deng Yanhua Tan Zhong Xie Minghong Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent Advances in Nonlinear Analysis dirichlet-to-neumann operator critical exponent blowup concentration phenomenon 35k55 35b33 35b40 35b44 |
| title | Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent |
| title_full | Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent |
| title_fullStr | Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent |
| title_full_unstemmed | Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent |
| title_short | Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent |
| title_sort | nonlinear elliptic parabolic problem involving p dirichlet to neumann operator with critical exponent |
| topic | dirichlet-to-neumann operator critical exponent blowup concentration phenomenon 35k55 35b33 35b40 35b44 |
| url | https://doi.org/10.1515/anona-2022-0306 |
| work_keys_str_mv | AT dengyanhua nonlinearellipticparabolicprobleminvolvingpdirichlettoneumannoperatorwithcriticalexponent AT tanzhong nonlinearellipticparabolicprobleminvolvingpdirichlettoneumannoperatorwithcriticalexponent AT xieminghong nonlinearellipticparabolicprobleminvolvingpdirichlettoneumannoperatorwithcriticalexponent |