Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations
Abstract In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first...
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SpringerOpen
2021-01-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-020-01482-6 |
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doaj-39460c99157c48a5acb4efaf022a8e472021-01-10T12:59:24ZengSpringerOpenBoundary Value Problems1687-27702021-01-012021112410.1186/s13661-020-01482-6Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equationsLiming Xiao0Mingkun Li1School of Mathematics and Systems Science, Guangdong Polytechnic Normal UniversitySchool of Mathematics and Systems Science, Guangdong Polytechnic Normal UniversityAbstract In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.https://doi.org/10.1186/s13661-020-01482-6Nonlinear pseudo-parabolic equationHigher-orderThe method of potential wellStatic problemExistence of global weak solution |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Liming Xiao Mingkun Li |
| spellingShingle |
Liming Xiao Mingkun Li Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations Boundary Value Problems Nonlinear pseudo-parabolic equation Higher-order The method of potential well Static problem Existence of global weak solution |
| author_facet |
Liming Xiao Mingkun Li |
| author_sort |
Liming Xiao |
| title |
Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations |
| title_short |
Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations |
| title_full |
Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations |
| title_fullStr |
Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations |
| title_full_unstemmed |
Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations |
| title_sort |
initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations |
| publisher |
SpringerOpen |
| series |
Boundary Value Problems |
| issn |
1687-2770 |
| publishDate |
2021-01-01 |
| description |
Abstract In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem. |
| topic |
Nonlinear pseudo-parabolic equation Higher-order The method of potential well Static problem Existence of global weak solution |
| url |
https://doi.org/10.1186/s13661-020-01482-6 |
| work_keys_str_mv |
AT limingxiao initialboundaryvalueproblemforaclassofhigherorderndimensionalnonlinearpseudoparabolicequations AT mingkunli initialboundaryvalueproblemforaclassofhigherorderndimensionalnonlinearpseudoparabolicequations |
| _version_ |
1724341960107360256 |