Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions
A monotone iteration scheme for traveling waves based on ordered upper and lower solutions is derived for a class of nonlocal dispersal system with delay. Such system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species. An example of such sy...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2019-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/51/abstr.html |
| _version_ | 1817988457082912768 |
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| author | Qiuling Huang Xiaojie Hou |
| author_facet | Qiuling Huang Xiaojie Hou |
| author_sort | Qiuling Huang |
| collection | DOAJ |
| description | A monotone iteration scheme for traveling waves based on ordered upper
and lower solutions is derived for a class of nonlocal dispersal system
with delay. Such system can be used to study the competition among
nonlocally diffusive species and degenerately diffusive species.
An example of such system is studied in detail. We show the existence
of the traveling wave solutions for this system by this iteration scheme.
In addition, we study the minimal wave speed, uniqueness, strict
monotonicity and asymptotic behavior of the traveling wave solutions. |
| first_indexed | 2024-04-14T00:34:20Z |
| format | Article |
| id | doaj.art-c69a3cfd4eaa42a5ad8a8e35bb48c029 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-14T00:34:20Z |
| publishDate | 2019-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c69a3cfd4eaa42a5ad8a8e35bb48c0292022-12-22T02:22:26ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-04-01201951,121Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusionsQiuling Huang0Xiaojie Hou1 Shandong Univ. of Finance and Economics, Jinan, China Univ. of North Carolina Wilmington, NC, USA A monotone iteration scheme for traveling waves based on ordered upper and lower solutions is derived for a class of nonlocal dispersal system with delay. Such system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species. An example of such system is studied in detail. We show the existence of the traveling wave solutions for this system by this iteration scheme. In addition, we study the minimal wave speed, uniqueness, strict monotonicity and asymptotic behavior of the traveling wave solutions.http://ejde.math.txstate.edu/Volumes/2019/51/abstr.htmlNonlocal diffusiontraveling wave solutionasymptoticsSchauder fixed point theoremupper and lower solutionsuniqueness |
| spellingShingle | Qiuling Huang Xiaojie Hou Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions Electronic Journal of Differential Equations Nonlocal diffusion traveling wave solution asymptotics Schauder fixed point theorem upper and lower solutions uniqueness |
| title | Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions |
| title_full | Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions |
| title_fullStr | Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions |
| title_full_unstemmed | Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions |
| title_short | Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions |
| title_sort | monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions |
| topic | Nonlocal diffusion traveling wave solution asymptotics Schauder fixed point theorem upper and lower solutions uniqueness |
| url | http://ejde.math.txstate.edu/Volumes/2019/51/abstr.html |
| work_keys_str_mv | AT qiulinghuang monotoneiterationschemeanditsapplicationtopartialdifferentialequationsystemswithmixednonlocalanddegeneratediffusions AT xiaojiehou monotoneiterationschemeanditsapplicationtopartialdifferentialequationsystemswithmixednonlocalanddegeneratediffusions |