Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case
It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in 2017 have obtained a blow-up result not only for super-Fujita exponent but also for the one closely related to Strauss exponent when the damp...
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| Veröffentlicht in: | Nonlinear analysis 2018-03, Vol.168, p.222-237 |
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| creator | Lai, Ning-An Takamura, Hiroyuki |
| description | It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in 2017 have obtained a blow-up result not only for super-Fujita exponent but also for the one closely related to Strauss exponent when the damping is scaling invariant and its constant is relatively small, which has been recently extended by Ikeda and Sobajima.
Introducing a multiplier for the time-derivative of the spatial integral of unknown functions, we succeed in employing the techniques on the analysis for semilinear wave equations and proving a blow-up result for semilinear damped wave equations with sub-Strauss exponent when the damping is in the scattering range. |
| doi_str_mv | 10.1016/j.na.2017.12.008 |
| format | Article |
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Introducing a multiplier for the time-derivative of the spatial integral of unknown functions, we succeed in employing the techniques on the analysis for semilinear wave equations and proving a blow-up result for semilinear damped wave equations with sub-Strauss exponent when the damping is in the scattering range.</description><subject>Blow-up</subject><subject>Damped wave equation</subject><subject>Damping</subject><subject>Derivatives</subject><subject>Integrals</subject><subject>Lifespan</subject><subject>Mathematical analysis</subject><subject>Scattering</subject><subject>Semilinear</subject><subject>Studies</subject><subject>Wave equations</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAQhi0EEqWwM1piTjjbiZOyQcWXVIkFJBZkOc6FOkqd1HZa-PcElZXphnue904vIZcMUgZMXrep0ykHVqSMpwDlEZmxshBJzll-TGYgJE_yTL6fkrMQWoCJFHJGPu66fp-MA216TwNubGcdak9rvRmwpnu9Q4rbUUfbu0D3Nq5pGCvjbbRGdxS_ht6hi9Q6GtdIg9Exorfukxod8JycNLoLePE35-Tt4f51-ZSsXh6fl7erxAjOYyJQFguTMQEIhcbC6GqRS1Gaii9YBWbRZNAgr3Rd6FrnlQGGspSVKACbGqSYk6tD7uD77YghqrYfvZtOKj6ti0yWIp8oOFDG9yF4bNTg7Ub7b8VA_ZaoWuW0-i1RMa6mEifl5qDg9P3OolfBWHQGa-vRRFX39n_5B7jjeqQ</recordid><startdate>201803</startdate><enddate>201803</enddate><creator>Lai, Ning-An</creator><creator>Takamura, Hiroyuki</creator><general>Elsevier Ltd</general><general>Elsevier BV</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>201803</creationdate><title>Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case</title><author>Lai, Ning-An ; Takamura, Hiroyuki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-3e679c4130e07ae7cab95638cb291b0c9f40fe2bad7ada5bc01e686b370efd063</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Blow-up</topic><topic>Damped wave equation</topic><topic>Damping</topic><topic>Derivatives</topic><topic>Integrals</topic><topic>Lifespan</topic><topic>Mathematical analysis</topic><topic>Scattering</topic><topic>Semilinear</topic><topic>Studies</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lai, Ning-An</creatorcontrib><creatorcontrib>Takamura, Hiroyuki</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>Lai, Ning-An</au><au>Takamura, Hiroyuki</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case</atitle><jtitle>Nonlinear analysis</jtitle><date>2018-03</date><risdate>2018</risdate><volume>168</volume><spage>222</spage><epage>237</epage><pages>222-237</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><abstract>It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in 2017 have obtained a blow-up result not only for super-Fujita exponent but also for the one closely related to Strauss exponent when the damping is scaling invariant and its constant is relatively small, which has been recently extended by Ikeda and Sobajima.
Introducing a multiplier for the time-derivative of the spatial integral of unknown functions, we succeed in employing the techniques on the analysis for semilinear wave equations and proving a blow-up result for semilinear damped wave equations with sub-Strauss exponent when the damping is in the scattering range.</abstract><cop>Elmsford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2017.12.008</doi><tpages>16</tpages></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Blow-up Damped wave equation Damping Derivatives Integrals Lifespan Mathematical analysis Scattering Semilinear Studies Wave equations |
| title | Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case |
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