Blow-up for Strauss type wave equation with damping and potential

We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear t...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-10
Main Authors: Dai, Wei, Kubo, Hideo, Sobajima, Motohiro
Format: Article
Language:English
Subjects:
Damping
Nonlinear equations
Upper bounds
Wave equations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Dai, Wei
Kubo, Hideo
Sobajima, Motohiro
description We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.
doi_str_mv 10.48550/arxiv.1909.08885
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2294292243</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2294292243</sourcerecordid><originalsourceid>FETCH-LOGICAL-a523-13a09aaf8d03f3b45ac2d0eb106aaae77892ab2dbe5d868ad1424ab53c650ef83</originalsourceid><addsrcrecordid>eNotzU9LwzAYgPEgCI65D-At4Ln1zZukTY5z-A8GHtx9vF1S7ahJ16SrfnsFPT2338PYjYBSGa3hjsav7lwKC7YEY4y-YAuUUhRGIV6xVUpHAMCqRq3lgq3v-zgX08DbOPK3PNKUEs_fg-cznT33p4lyFwOfu_zBHX0OXXjnFBwfYvYhd9Rfs8uW-uRX_12y3ePDbvNcbF-fXjbrbUEaZSEkgSVqjQPZykZpOqAD3wioiMjXtbFIDbrGa2cqQ04oVNRoeag0-NbIJbv9Y4cxniaf8v4YpzH8HveIVqFFVFL-ABHLS_M</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2294292243</pqid></control><display><type>article</type><title>Blow-up for Strauss type wave equation with damping and potential</title><source>Publicly Available Content Database</source><creator>Dai, Wei ; Kubo, Hideo ; Sobajima, Motohiro</creator><creatorcontrib>Dai, Wei ; Kubo, Hideo ; Sobajima, Motohiro</creatorcontrib><description>We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1909.08885</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Damping ; Nonlinear equations ; Upper bounds ; Wave equations</subject><ispartof>arXiv.org, 2020-10</ispartof><rights>2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2294292243?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,27925,37012,44590</link.rule.ids></links><search><creatorcontrib>Dai, Wei</creatorcontrib><creatorcontrib>Kubo, Hideo</creatorcontrib><creatorcontrib>Sobajima, Motohiro</creatorcontrib><title>Blow-up for Strauss type wave equation with damping and potential</title><title>arXiv.org</title><description>We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.</description><subject>Damping</subject><subject>Nonlinear equations</subject><subject>Upper bounds</subject><subject>Wave equations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNotzU9LwzAYgPEgCI65D-At4Ln1zZukTY5z-A8GHtx9vF1S7ahJ16SrfnsFPT2338PYjYBSGa3hjsav7lwKC7YEY4y-YAuUUhRGIV6xVUpHAMCqRq3lgq3v-zgX08DbOPK3PNKUEs_fg-cznT33p4lyFwOfu_zBHX0OXXjnFBwfYvYhd9Rfs8uW-uRX_12y3ePDbvNcbF-fXjbrbUEaZSEkgSVqjQPZykZpOqAD3wioiMjXtbFIDbrGa2cqQ04oVNRoeag0-NbIJbv9Y4cxniaf8v4YpzH8HveIVqFFVFL-ABHLS_M</recordid><startdate>20201009</startdate><enddate>20201009</enddate><creator>Dai, Wei</creator><creator>Kubo, Hideo</creator><creator>Sobajima, Motohiro</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20201009</creationdate><title>Blow-up for Strauss type wave equation with damping and potential</title><author>Dai, Wei ; Kubo, Hideo ; Sobajima, Motohiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a523-13a09aaf8d03f3b45ac2d0eb106aaae77892ab2dbe5d868ad1424ab53c650ef83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Damping</topic><topic>Nonlinear equations</topic><topic>Upper bounds</topic><topic>Wave equations</topic><toplevel>online_resources</toplevel><creatorcontrib>Dai, Wei</creatorcontrib><creatorcontrib>Kubo, Hideo</creatorcontrib><creatorcontrib>Sobajima, Motohiro</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dai, Wei</au><au>Kubo, Hideo</au><au>Sobajima, Motohiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Blow-up for Strauss type wave equation with damping and potential</atitle><jtitle>arXiv.org</jtitle><date>2020-10-09</date><risdate>2020</risdate><eissn>2331-8422</eissn><abstract>We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1909.08885</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2020-10
issn 2331-8422
language eng
recordid cdi_proquest_journals_2294292243
source Publicly Available Content Database
subjects Damping
Nonlinear equations
Upper bounds
Wave equations
title Blow-up for Strauss type wave equation with damping and potential
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T21%3A10%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Blow-up%20for%20Strauss%20type%20wave%20equation%20with%20damping%20and%20potential&rft.jtitle=arXiv.org&rft.au=Dai,%20Wei&rft.date=2020-10-09&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1909.08885&rft_dat=%3Cproquest%3E2294292243%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a523-13a09aaf8d03f3b45ac2d0eb106aaae77892ab2dbe5d868ad1424ab53c650ef83%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2294292243&rft_id=info:pmid/&rfr_iscdi=true