Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions
In this paper, we devote to studying the blow-up phenomena for a porous medium equation under nonlocal boundary conditions. Based on auxiliary functions and differential inequality technique, we derive the sufficient conditions to guarantee the existence of blow-up solutions under different measures...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9037287 |
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| _version_ | 1832568518009159680 |
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| author | Huimin Tian Lingling Zhang |
| author_facet | Huimin Tian Lingling Zhang |
| author_sort | Huimin Tian |
| collection | DOAJ |
| description | In this paper, we devote to studying the blow-up phenomena for a porous medium equation under nonlocal boundary conditions. Based on auxiliary functions and differential inequality technique, we derive the sufficient conditions to guarantee the existence of blow-up solutions under different measures and obtain an upper bound for blow-up time. Moreover, we demonstrate the lower bounds for blow-up time under some appropriate measures in R3 and in the higher-dimensional space Rnn≥3, respectively. At last, two examples are given to illustrate the applications of main results. |
| format | Article |
| id | doaj-art-adb9eacc768544a08907734be4b459c3 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-adb9eacc768544a08907734be4b459c32025-02-03T00:58:57ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/90372879037287Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary ConditionsHuimin Tian0Lingling Zhang1Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, ChinaIn this paper, we devote to studying the blow-up phenomena for a porous medium equation under nonlocal boundary conditions. Based on auxiliary functions and differential inequality technique, we derive the sufficient conditions to guarantee the existence of blow-up solutions under different measures and obtain an upper bound for blow-up time. Moreover, we demonstrate the lower bounds for blow-up time under some appropriate measures in R3 and in the higher-dimensional space Rnn≥3, respectively. At last, two examples are given to illustrate the applications of main results.http://dx.doi.org/10.1155/2020/9037287 |
| spellingShingle | Huimin Tian Lingling Zhang Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions Complexity |
| title | Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions |
| title_full | Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions |
| title_fullStr | Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions |
| title_full_unstemmed | Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions |
| title_short | Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions |
| title_sort | blow up solution of a porous medium equation with nonlocal boundary conditions |
| url | http://dx.doi.org/10.1155/2020/9037287 |
| work_keys_str_mv | AT huimintian blowupsolutionofaporousmediumequationwithnonlocalboundaryconditions AT linglingzhang blowupsolutionofaporousmediumequationwithnonlocalboundaryconditions |