Browsing by Author "Makino, T"

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On spherically symmetric solutions of the relativistic Euler equation
(2004-06-20)
Hsu, CH
;
Lin, SS
;
Makino, T
;
應用數學系
;
Department of Applied Mathematics
This work investigates the spherical symmetric solutions of more realistic equation of states. We generalize the method of Hsu et al. (Methods Appl. Anal. 8 (2001) 159) to show the existence of spherical symmetric weak Solution of the relativistic Euler equation with initial data containing the vacuum state. (C) 2004 Elsevier Inc. All rights reserved.
Smooth solutions to a class of quasilinear wave equations
(2006-05-15)
Hsu, CH
;
Lin, SS
;
Makino, T
;
應用數學系
;
Department of Applied Mathematics
This article investigates the existence/nonexistence of smooth solutions of nonlinear vibration equations which arise from the one-dimensional motion of polytropic gas without external forces contained in a finite interval. For any fixed arbitrarily long time, we show that there are smooth small amplitude solutions of the nonlinear equations for which the periodic solutions of the linearized equation are the first-order approximations. On the other hand, when the nonlinearity is strictly convex or concave, there exists no time-periodic solutions which are twice continuously differentiable. An example of possible singularities which occur at the second derivatives is illustrated. We also give another kind of exact solutions with singularity such that shocks occur after a finite time. Furthermore, we get an estimate of the life span of smooth solutions to the initial-boundary value problem. (c) 2005 Elsevier Inc. All rights reserved.