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| NONLINEAR PSEUDOPARABOLIC EQUATIONS IN ARBITRARY DIMENSIONS | |
| 引用本文： | 刘亚成,万维明,吕淑娟. NONLINEAR PSEUDOPARABOLIC EQUATIONS IN ARBITRARY DIMENSIONS[J]. 应用数学学报(英文版), 1997, 13(3): 265-278. DOI: 10.1007/BF02025882 |
| 作者姓名： | 刘亚成 万维明 吕淑娟 |
| 作者单位： | LIU YACHENG (Department of Mathematics and Mechanics，Harbin Engineering University，Harbin 150001，China)WAN WEIMING (Department of Mathematics，Northeast Forestry University，Harbin 150040，China)LU SHUJUAN (Department of Foundation，Harbin Medical Univ |
| 摘 要： | 1.IntroductionAsiswellknownthenonlinearpseudoparabolicequationsweresuggestedandstudiedinconnectionwithmanypracticalproblemsatthebeginningofthe1970s.AmongthemtheBBMequationat box~abet~0(1'1)isthemostimportant,itwassuggestedinconnectionwiththepropagationoflongwavesinnonlineardispersivesystemsbyT.B.Benjaminetallljin1972.In1977,L.A.Medeirosetall2]studiedtheweaksolutionoftheinitialboundaryvalueproblemforageneralizedformof(1.1)RevisedJanuary,25,1995.*ThisworkissupportedbytheNationalScienceFOun… |
Nonlinear pseudoparabolic equations in arbitrary dimensions |
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| Yacheng Liu,Weiming Wan,Shujuan Lü. Nonlinear pseudoparabolic equations in arbitrary dimensions[J]. Acta Mathematicae Applicatae Sinica, 1997, 13(3): 265-278. DOI: 10.1007/BF02025882 | |
| Authors: | Yacheng Liu Weiming Wan Shujuan Lü |
| Affiliation: | 1. Department of Mathematics and Mechanics, Harbin Engineering University, 150001, Harbin, China 2. Department of Mathematics, Northeast Forestry University, 150040, Harbin, China 3. Department of Foundation, Harbin Medical University, 150086, Harbin, China |
| Abstract: | In this paper, we study the existence and uniqueness of the global generalized solution and strong solution of the initial-boundary value problem and the corresponding initial value problem for the nonlinear pseudoparabolic equation in arbitrary dimensions Besides, the smoothness, asymptotic behaviors and blow-up of the solutions are also discussed.The results not only include but also improve and generalize the main results concerning this class of equations. |
| Keywords: | Nonlinear pseudoparabolic equation L_2 estimates global solution |
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