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dc.contributor.authorLin, SSen_US
dc.date.accessioned2019-04-03T06:38:49Z-
dc.date.available2019-04-03T06:38:49Z-
dc.date.issued1997-05-01en_US
dc.identifier.issn0036-1410en_US
dc.identifier.urihttp://dx.doi.org/10.1137/S0036141095292883en_US
dc.identifier.urihttp://hdl.handle.net/11536/149509-
dc.description.abstractWe study the linearized stability of stationary solutions of gaseous stars which are in spherically symmetric and isentropic motion. If viscosity is ignored, we have following three types of problems: (EC), Euler equation with a solid core; (EP), Euler-Poisson equation without a solid core; (EPC), Euler-Poisson equation with a solid core. In Lagrangian formulation, we prove that any solution of (EC) is neutrally stable. Any solution of (EP) and (EPC) is also neutrally stable when the adiabatic index gamma is an element of (4/3,2) and unstable for (EP) when gamma is an element of (1, 4/3). Moreover, for (EPC) and gamma is an element of (1, 2), any solution with small total mass is also neutrally stable. When viscosity is present (nu > 0), the velocity disturbance on the outer surface of gas is important. For nu > 0, we prove that the neutrally stable solution (when nu = 0) is now stable with respect to positive-type disturbances, which include Dirichlet and Neumann boundary conditions. The solution can be unstable with respect to disturbances of some other types. The problems were studied through spectral analysis of the linearized operators with singularities at the endpoints of intervals.en_US
dc.language.isoen_USen_US
dc.subjectstabilityen_US
dc.subjectisentropic gasen_US
dc.subjectself-gravitatingen_US
dc.subjectsolid coreen_US
dc.subjectlimit-point singularityen_US
dc.titleStability of gaseous stars in spherically symmetric motionsen_US
dc.typeArticleen_US
dc.identifier.doi10.1137/S0036141095292883en_US
dc.identifier.journalSIAM JOURNAL ON MATHEMATICAL ANALYSISen_US
dc.citation.volume28en_US
dc.citation.issue3en_US
dc.citation.spage539en_US
dc.citation.epage569en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:A1997WW98300004en_US
dc.citation.woscount45en_US
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