Global well-posedness of semilinear hyperbolic equations, parabolic equations and Schrodinger equations

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dc.contributor.authorXu, Runzhang
dc.contributor.authorChen, Yuxuan
dc.contributor.authorYang, Yanbing
dc.contributor.authorChen, Shaohua
dc.contributor.authorShen, Jihong
dc.contributor.authorYu, Tao
dc.contributor.authorXu, Zhengsheng
dc.date.accessioned2022-01-10T14:18:22Z
dc.date.available2022-01-10T14:18:22Z
dc.date.issued2018-02-23
dc.description.abstractThis article studies the existence and nonexistence of global solutions to the initial boundary value problems for semilinear wave and heat equation, and for Cauchy problem of nonlinear Schrödinger equation. This is done under three possible initial energy levels, except the NLS as it does not have comparison principle. The most important feature in this article is a new hypothesis on the nonlinear source terms which can include at least eight important and popular power-type nonlinearities as special cases. This article also finds some kinds of divisions for the initial data to guarantee the global existence or finite time blowup of the solution of the above three problems.
dc.description.departmentMathematics
dc.formatText
dc.format.extent52 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationXu, R., Chen, Y., Yang, Y., Chen, S., Shen, J., Yu, T., & Xu, Z. (2018). Global well-posedness of semilinear hyperbolic equations, parabolic equations and Schrodinger equations. <i>Electronic Journal of Differential Equations, 2018</i>(55), pp. 1-52.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15111
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSemilinear hyperbolic equation
dc.subjectSemilinear parabolic equation
dc.subjectNonlinear Schrödinger equation
dc.subjectGlobal solution
dc.subjectPotential well
dc.titleGlobal well-posedness of semilinear hyperbolic equations, parabolic equations and Schrodinger equations
dc.typeArticle

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