Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations
In this paper we study the global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, utt−Luxx=B(−|u|p−1u)xx,(p>1), where the nonlocality enters through two pseudo-differential operators L and B. We establish thresholds for g...
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| Veröffentlicht in: | Nonlinear analysis 2014-01, Vol.95, p.313-322 |
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| creator | Erbay, H.A. Erbay, S. Erkip, A. |
| description | In this paper we study the global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, utt−Luxx=B(−|u|p−1u)xx,(p>1), where the nonlocality enters through two pseudo-differential operators L and B. We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. Our results improve the global existence and blow-up results given in the literature for the present class of nonlocal nonlinear wave equations and cover those given for many well-known nonlinear dispersive wave equations such as the so-called double-dispersion equation and the traditional Boussinesq-type equations, as special cases. |
| doi_str_mv | 10.1016/j.na.2013.09.013 |
| format | Article |
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We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. 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We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. Our results improve the global existence and blow-up results given in the literature for the present class of nonlocal nonlinear wave equations and cover those given for many well-known nonlinear dispersive wave equations such as the so-called double-dispersion equation and the traditional Boussinesq-type equations, as special cases.</description><subject>Blow-up</subject><subject>Boussinesq equation</subject><subject>Double dispersion equation</subject><subject>Global existence</subject><subject>Mathematical analysis</subject><subject>Nonlocal Cauchy problem</subject><subject>Potential well</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAQhi0EEqWwM3pkSbCT2EnYUMWXhMRSJDbLsS_gYuzWl7Tw70lVVqZXp3vek-4h5JKznDMur1d50HnBeJmzNp_iiMx4U5eZKLg4JjNWyiITlXw7JWeIK8YYr0s5I5_LjwT4Eb1F2sdE333stKfw7XCAYIDqYGnn4y4b19QFquk7BEgTYrxGpLGnNo6d_6HW4RoSui3QEIOPZmJ2eppgM-rBxYDn5KTXHuHiL-fk9f5uuXjMnl8enha3z5kpZTtkIGoOLZeMs0KAqa0Q3FRV1UjbtbYu-X7RV7w3tul13zQts1UnOwuttC2Dck6uDnfXKW5GwEF9OTTgvQ4QR1RcMFk2opFiQtkBNSkiJujVOrkvnX4UZ2rvVa1U0GrvVbFWTTFVbg4VmF7YOkgKjdursi6BGZSN7v_yL3crgN4</recordid><startdate>201401</startdate><enddate>201401</enddate><creator>Erbay, H.A.</creator><creator>Erbay, S.</creator><creator>Erkip, A.</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201401</creationdate><title>Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations</title><author>Erbay, H.A. ; Erbay, S. ; Erkip, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c369t-e571e91601025ec7d551c44486db9d7310102f41fcd8faf8890d4b6bde96d90e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Blow-up</topic><topic>Boussinesq equation</topic><topic>Double dispersion equation</topic><topic>Global existence</topic><topic>Mathematical analysis</topic><topic>Nonlocal Cauchy problem</topic><topic>Potential well</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Erbay, H.A.</creatorcontrib><creatorcontrib>Erbay, S.</creatorcontrib><creatorcontrib>Erkip, A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Erbay, H.A.</au><au>Erbay, S.</au><au>Erkip, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations</atitle><jtitle>Nonlinear analysis</jtitle><date>2014-01</date><risdate>2014</risdate><volume>95</volume><spage>313</spage><epage>322</epage><pages>313-322</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><abstract>In this paper we study the global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, utt−Luxx=B(−|u|p−1u)xx,(p>1), where the nonlocality enters through two pseudo-differential operators L and B. 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| source | Elsevier ScienceDirect Journals |
| subjects | Blow-up Boussinesq equation Double dispersion equation Global existence Mathematical analysis Nonlocal Cauchy problem Potential well |
| title | Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations |
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