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Keywords:
abstract hyperbolic equations; Rothe method
abstract hyperbolic equations; Rothe method
Summary:
In this paper abstract hyperbolic equations in which elliptic operator dependent on time is involved are solved by using the so callad Rothe method, i.e. the method of discretisation of given problem in time. Existence and unicity of solution and some of its properties in dependence on various conditions which the given equations satisfy are presented.
References:
[1] K. Rektorys: On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables. Czech. Math. J. 21 (1971), pp. 318-339. MR 0298237 | Zbl 0217.41601
[2] J. Kačur: Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order. Czech. Math. J. 28 (1978), pp. 507-524. MR 0506431
[3] J. Kačur: Application of Rothe's method to nonlinear equations. Math. čas. 25 (1975), pp. 63-81. MR 0394344
[4] J. Kačur A. Wawruch: On an approximate solution for quasilinear parabolic eguations. Czech. Math. J. 27 (1977), pp. 220-241. MR 0605665
[5] J. Nečas: Application of Rothe's method to abstract parabolic equations. Czech. Math. J. 24 (1974), pp. 496-500. MR 0348571 | Zbl 0311.35059
[6] M. Pultar: Nonlinear parabolic problems with maximal monotone operators solved by the method of discretization in time. Dissertation. (In Czech.)
[7] J. Streiblová: Solution of hyperbolic problems by the Rothe method. Habilitation. Bull. of the Faculty of Civil Engineering in Prague (To appear.)
[8] F. Bubeník: A note to the solution of hyperbolic problems by the Rothe method. Dissertation. Bull, of the Faculty of Civil Engineering in Prague. (To appear.)
[9] E. Rothe: Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben. Math. Ann. 102, 1930. DOI 10.1007/BF01782368 | MR 1512599
[10] J. Lions L. Magenes: Problèmes aux limites non homogènes et applications. Dunod, Paris, 1968.
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