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ID：51940440
大小：496.72 KB
页数：40页
时间：2020-03-19
《非线性的粘弹性波动方程(组)的解的性质.pdf》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
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6、E2v& R+ l7、uB3H1Ums(up7?zuZUa2e2_zW2ZV s(Z2sW%U6℄uw?VarzU0[=V up7U?u8、u9、γ−2.tt0b?o~Uy7;ub1% UÆ#om{af2bY9krz10、p URDirichletCy7Us(h('^p7Zt11、u12、ju−∆u−∆u+g(t−s)∆u(x,s)ds+13、u14、m−1u=f(u,v)ttttttt10Zt15、v16、jv−∆v−∆v+h(t−s)∆v(x,s)ds+17、v18、r−1v=f(u,v)ttttttt20{a UaUpk;ubRh( U;AUom;? d4({a&of Rd4).?C&t)Vi)r9k=E4!Dz8}g3e5i'}HlH2gT2zAbstractAlongwiths19、cience’sandtechnology’sdevelopment,variousnon-linearprob-lemhavearousedpeople’swidespreadattention.Theboundaryproblemofnon-linearpartialdifferentialequation(equations)originatefromappliedmathemat-ics,physics,controltheoryandotherapplieddisciplines,itispresentlyon20、eofthemostactiveresearchtopicsinnonlinearsciencefield,anditishottopicinrecentyears,anditisaquiteimportantfieldofthepartialdifferentialequations.Inthispaper,usingthemultipliermethod,auxiliaryfunctionandthepoten-tialwellmethod,westudythepropertiesofthesolutionsfornon21、linearviscoelasticwaveequation(equations).Thethesisisdividedintotherechapters.Inchapter1,weintroducetheresearchcurrentsituationandthemainresultsofthediscussingprobleminthispaper.Inchapter2,weconsiderthenonlinearviscoelasticwaveequationZtγ−2utt−∆u+g(t−s)∆u(s)ds=u22、23、u24、0withacousticboundaryconditions.Weprovethattheenergywillgrowupasanexponentialfunctionastimegoestoinfinity,providethattheinitialenergyisnegative.Inchapter3,weconside
7、uB3H1Ums(up7?zuZUa2e2_zW2ZV s(Z2sW%U6℄uw?VarzU0[=V up7U?u8、u9、γ−2.tt0b?o~Uy7;ub1% UÆ#om{af2bY9krz10、p URDirichletCy7Us(h('^p7Zt11、u12、ju−∆u−∆u+g(t−s)∆u(x,s)ds+13、u14、m−1u=f(u,v)ttttttt10Zt15、v16、jv−∆v−∆v+h(t−s)∆v(x,s)ds+17、v18、r−1v=f(u,v)ttttttt20{a UaUpk;ubRh( U;AUom;? d4({a&of Rd4).?C&t)Vi)r9k=E4!Dz8}g3e5i'}HlH2gT2zAbstractAlongwiths19、cience’sandtechnology’sdevelopment,variousnon-linearprob-lemhavearousedpeople’swidespreadattention.Theboundaryproblemofnon-linearpartialdifferentialequation(equations)originatefromappliedmathemat-ics,physics,controltheoryandotherapplieddisciplines,itispresentlyon20、eofthemostactiveresearchtopicsinnonlinearsciencefield,anditishottopicinrecentyears,anditisaquiteimportantfieldofthepartialdifferentialequations.Inthispaper,usingthemultipliermethod,auxiliaryfunctionandthepoten-tialwellmethod,westudythepropertiesofthesolutionsfornon21、linearviscoelasticwaveequation(equations).Thethesisisdividedintotherechapters.Inchapter1,weintroducetheresearchcurrentsituationandthemainresultsofthediscussingprobleminthispaper.Inchapter2,weconsiderthenonlinearviscoelasticwaveequationZtγ−2utt−∆u+g(t−s)∆u(s)ds=u22、23、u24、0withacousticboundaryconditions.Weprovethattheenergywillgrowupasanexponentialfunctionastimegoestoinfinity,providethattheinitialenergyisnegative.Inchapter3,weconside
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19、cience’sandtechnology’sdevelopment,variousnon-linearprob-lemhavearousedpeople’swidespreadattention.Theboundaryproblemofnon-linearpartialdifferentialequation(equations)originatefromappliedmathemat-ics,physics,controltheoryandotherapplieddisciplines,itispresentlyon
20、eofthemostactiveresearchtopicsinnonlinearsciencefield,anditishottopicinrecentyears,anditisaquiteimportantfieldofthepartialdifferentialequations.Inthispaper,usingthemultipliermethod,auxiliaryfunctionandthepoten-tialwellmethod,westudythepropertiesofthesolutionsfornon
21、linearviscoelasticwaveequation(equations).Thethesisisdividedintotherechapters.Inchapter1,weintroducetheresearchcurrentsituationandthemainresultsofthediscussingprobleminthispaper.Inchapter2,weconsiderthenonlinearviscoelasticwaveequationZtγ−2utt−∆u+g(t−s)∆u(s)ds=u
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24、0withacousticboundaryconditions.Weprovethattheenergywillgrowupasanexponentialfunctionastimegoestoinfinity,providethattheinitialenergyisnegative.Inchapter3,weconside
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