논문KCI 등재
SOLUTIONS OF QUASILINEAR WAVE EQUATION WITH STRONG AND NONLINEAR VISCOSITY
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초록
We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.
Abstract
We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.
참고문헌 (13)
- H. T. Banks, "Smart Material Structures, Modeling, Esti- mation and Control, RAM" (1996), John Wiley and Sons
- R. Dautray, "Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5, Evolution Problems I" (1992), Springer-Verlag
- D. Gilbarg, "Elliptic Partial Differential Equations of Second Order" (1977), Springer-Verlag
- J. Greenberg, "On the existence, uniqueness, and stability of solutions of the equation 0Xtt = E(Xx)Xxx + λXxxt", J. Math. Anal. Appl, 25, pp.575~591 (1969)
- J. Greenberg, "On the existence, uniqueness, and stability of solutions of the equation ′ (ux)uxx + λuxtx = 0utt", J. Math. Mech, 17, pp.707~728 (1968)
- J.-H.Ha, "Frechet differentiability of solution mappings for semilinear second order evolution equations", J. Math. Anal. Appl, 346(2), pp.374~383 (2008)
- 황진수, "Weak solutions of the equation of motion of membrane with strong viscosity", 대한수학회지, 44(2), pp.443~453 (2007), 대한수학회
- J. S. Hwang, "Optimal control problems for the equation of motion of membrane with strong viscosity", J. Math. Anal. Appl, 321(1), pp.327~342 (2006)
- J. S. Hwang, "Parameter identication problems for the equation of motion of membrane with strong viscosity", J. Math. Anal. Appl, 342(1), pp.125~134 (2008)
- T. Kobayashi, "On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity", Math. Ann, 296(2), pp.215~234 (1993)
- R. E. Showalter, "Hilbert Space Method for Partial Differential Equations" (1977), Pitman
- R. Temam, "Infnite-Dimensional Dynamical Systems in Mechanics and Physis, Second Edition, Applied Mathematical Sciences. Vol. 68" (1997), Springer-Verlag
- Q.-F. Wang, "Weak solutions of nonlinear parabolic evolution problems with uniform Lipschitz continuous nonlinearities", Mem. Grad. School Sci. & Technol, 19, pp.83~96 (2001), Kobe Univ
관련 논문AI추천
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