The Existence and Uniqueness of Global Admissible Conservative Weak Solution for the Periodic Single-Cycle Pulse Equation
This paper is devoted to studying the existence and uniqueness of global admissible conservative weak solution for the periodic single-cycle pulse equation without any additional assumptions. Firstly, introducing a new set of variables, we transform the single-cycle pulse equation into an equivalent...
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| Veröffentlicht in: | Journal of mathematical fluid mechanics 2022-08, Vol.24 (3), Article 57 |
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| creator | Guo, Yingying Yin, Zhaoyang |
| description | This paper is devoted to studying the existence and uniqueness of global admissible conservative weak solution for the periodic single-cycle pulse equation without any additional assumptions. Firstly, introducing a new set of variables, we transform the single-cycle pulse equation into an equivalent semilinear system. Using the standard ordinary differential equation theory, the global solution of the semilinear system is studied. Secondly, returning to the original coordinates, we get a global admissible conservative weak solution for the periodic single-cycle pulse equation. Finally, choosing some vital test functions which are different from [Bressan (Discrete Contin. Dyn. Syst 35:25-42, 2015), Brunelli (Phys. Lett. A 353:475-478, 2006)], we find a equation to single out a unique characteristic curve through each initial point. Moreover, the uniqueness of global admissible conservative weak solution is obtained. |
| doi_str_mv | 10.1007/s00021-022-00691-6 |
| format | Article |
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Firstly, introducing a new set of variables, we transform the single-cycle pulse equation into an equivalent semilinear system. Using the standard ordinary differential equation theory, the global solution of the semilinear system is studied. Secondly, returning to the original coordinates, we get a global admissible conservative weak solution for the periodic single-cycle pulse equation. Finally, choosing some vital test functions which are different from [Bressan (Discrete Contin. Dyn. Syst 35:25-42, 2015), Brunelli (Phys. Lett. A 353:475-478, 2006)], we find a equation to single out a unique characteristic curve through each initial point. 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Math. Fluid Mech</addtitle><description>This paper is devoted to studying the existence and uniqueness of global admissible conservative weak solution for the periodic single-cycle pulse equation without any additional assumptions. Firstly, introducing a new set of variables, we transform the single-cycle pulse equation into an equivalent semilinear system. Using the standard ordinary differential equation theory, the global solution of the semilinear system is studied. Secondly, returning to the original coordinates, we get a global admissible conservative weak solution for the periodic single-cycle pulse equation. Finally, choosing some vital test functions which are different from [Bressan (Discrete Contin. Dyn. Syst 35:25-42, 2015), Brunelli (Phys. Lett. A 353:475-478, 2006)], we find a equation to single out a unique characteristic curve through each initial point. Moreover, the uniqueness of global admissible conservative weak solution is obtained.</description><subject>Classical and Continuum Physics</subject><subject>Differential equations</subject><subject>Fluid mechanics</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical Methods in Physics</subject><subject>Ordinary differential equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Theoretical mathematics</subject><subject>Uniqueness</subject><issn>1422-6928</issn><issn>1422-6952</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhQdRsFb_gKuA69E8ppmZZRnqAwoW2uIyZDI3NXWatMlMsf_e1IruXN0H55zL_ZLkluB7gnH-EDDGlKSY0hRjXpKUnyUDksWRlyN6_tvT4jK5CmGNMclHJR0kh8U7oMmnCR1YBUjaBi2t2fVgIQTkNHpqXS1bNG42JgRTt4AqZwP4vezMHtAbyA80d23fGWeRdh51MXAG3rjGKDQ3dtVCWh1UNM76NsRju14exdfJhZZxcfNTh8nycbKontPp69NLNZ6miua4S7Ucac3yOmNNo5nORwRywkBRWTdU5kqzushqyUFmpCBAMmCcacUVLQre1A0bJnen3K138a_QibXrvY0nBeWRAS84L6OKnlTKuxA8aLH1ZiP9QRAsjojFCbGIiMU3YsGjiZ1MIYrtCvxf9D-uLyk5gNk</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Guo, Yingying</creator><creator>Yin, Zhaoyang</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-3199-7694</orcidid></search><sort><creationdate>20220801</creationdate><title>The Existence and Uniqueness of Global Admissible Conservative Weak Solution for the Periodic Single-Cycle Pulse Equation</title><author>Guo, Yingying ; Yin, Zhaoyang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-fa5ff37b43ddf3f751e713ec2abd2a7cf3b84ba6ea4181e14e363fc6c2886dbd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Classical and Continuum Physics</topic><topic>Differential equations</topic><topic>Fluid mechanics</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical Methods in Physics</topic><topic>Ordinary differential equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Theoretical mathematics</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guo, Yingying</creatorcontrib><creatorcontrib>Yin, Zhaoyang</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guo, Yingying</au><au>Yin, Zhaoyang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Existence and Uniqueness of Global Admissible Conservative Weak Solution for the Periodic Single-Cycle Pulse Equation</atitle><jtitle>Journal of mathematical fluid mechanics</jtitle><stitle>J. Math. Fluid Mech</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>24</volume><issue>3</issue><artnum>57</artnum><issn>1422-6928</issn><eissn>1422-6952</eissn><abstract>This paper is devoted to studying the existence and uniqueness of global admissible conservative weak solution for the periodic single-cycle pulse equation without any additional assumptions. Firstly, introducing a new set of variables, we transform the single-cycle pulse equation into an equivalent semilinear system. Using the standard ordinary differential equation theory, the global solution of the semilinear system is studied. Secondly, returning to the original coordinates, we get a global admissible conservative weak solution for the periodic single-cycle pulse equation. Finally, choosing some vital test functions which are different from [Bressan (Discrete Contin. Dyn. Syst 35:25-42, 2015), Brunelli (Phys. Lett. A 353:475-478, 2006)], we find a equation to single out a unique characteristic curve through each initial point. Moreover, the uniqueness of global admissible conservative weak solution is obtained.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00021-022-00691-6</doi><orcidid>https://orcid.org/0000-0003-3199-7694</orcidid></addata></record> |
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| subjects | Classical and Continuum Physics Differential equations Fluid mechanics Fluid- and Aerodynamics Mathematical Methods in Physics Ordinary differential equations Physics Physics and Astronomy Theoretical mathematics Uniqueness |
| title | The Existence and Uniqueness of Global Admissible Conservative Weak Solution for the Periodic Single-Cycle Pulse Equation |
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