Abstract
This Chapter extends, in so far as possible, the problems studied in Chapter 5 in the Hilbert space setting, to spaces of distributions or ultradistributions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Pozzi, G. A., Problemi di limiti per l’equazione della corda vibrante nell’ambito delle distribuzioni. Rend. Ist. Lombardo Sc. Lett. (A) 104, 534–579 (1970).
Pozzi, G. A., Ulteriori osservazioni sui problemi… Id. 105, 306–316 (1971).
Balaban, T., On the mixed problem for a hyperbolic equation. Mem. Amer. Math. Soc. 112 (1971).
Ikawa, M., Remarques sur les problèmes mixtes pour l’équation des ondes. Symp. C.N.R.S., Sept. 1972, Paris.
Kasahara, K., On weak well posedness of mixed problems for hyperbolic systems. Publ. R. I. M. S. Kyoto Univ. Vol. 6, 3, 1970.
Kato, J., Mixed problems of hyperbolic equations in a general domain. Proc. Jap. Acad. 47, 67–70 (1971).
Kreiss, H. O., Initial boundary value problems for hyperbolic systems. C. P. A. M. 13 (1970). Rauch, J.
Sakamoto, R., Mixed problems for hyperbolic equations (I) and (II). J. Math. Kyoto Univ. Vol. 10, 2 and 3.
Shirota, T., Agemi, R., On necessary and sufficient conditions for L2 well-posedness of mixed problems for hyperbolic equations. J. Fac. Sci. Hokkaido Univ. Vol. 21, 2, 1970.
Baouendi, M. S., Solution of P.D.E. in trace functions. Symp. C.N.R.S., Sept. 1972, Paris.
Bony, J. M., Schapira, P., Problème de Cauchy, existence et prolongement pour les hyperfonctions solutions des équations hyperboliques non strictes. C. R. A. S. Paris 274, 188–191 (1972).
Bony, J. M., Schapira, P., Solutions hyperfonctions du problème de Cauchy (to appear).
Kawai, T., Construction of elementary solutions of I-hyperbolic operators and solutions with small singularities. Proc. Japan Acad. 46, 912–915 (1970).
Komatsu, H., Kawai, T., Boundary values of hyperfunction solutions of linear partial differential equations. Publ. R. I. M. S. Kyoto Univ. 7, 95–104 (1971/1972).
Anderson, K. G., Propagation of analyticity of solutions of partial differential equations with constant coefficients. Ark. Mat. Vol. 8, 277–302 (1971).
de Giorgi, E., Cattabriga, L., Una dimostrazione diretta dell’esistenza di soluzioni analitiche nel piano reale di equazioni a derivate parziali a coefficienti costanti. Boll. dell’U. M. I. 4, 1015–1027 (1971).
Hörmander, L., Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients. Comm. Pure Appl. Math. 24, 671–703 (1971).
Kawai, T., On the global existence of real analytic solutions of linear differential equations (I), (II). Proc. Japan Acad. 47, 537–540 (1971).
Babuska, I., The finite element method with Lagrangian multipliers. Technical Note BN-724. Inst. Fluid Dyn. and Appl. Maths. Univ. of Maryland, January 1972.
Babuska, I., Kellog, R. B., Numerical solution of the neutron diffusion equation in the presence of corners and interfaces. Technical Note BN-720. Inst. Fluid Dyn. and Appl. Maths. Univ. of Maryland, December 1971.
Bramble, J. H., Variational methods for the numerical solution of elliptic problems. Lecture Notes Chalmers Inst. Technology 1970.
Bramble, J. H., Zlamal, M., Triangular elements in the finite element method. Math. Comp. 24, 112 809–820 (1970).
Brezzi, F., Sull ‘analisi numerica del problema di Dirichlet per le equazioni lineari ellittiche. Publicazione 18, Laboratorio di Analisi Numerica, Pavia, 1971.
Ciarlet, P. G., Raviart, P. A., General Lagrange and Hermite interpolation in R’b with applications to finite element methods. Arch. Rat. Mech. Anal. (to appear).
Ciarlet, P. G., Raviart, P. A., Interpolation theory over curved elements with applications to finite element methods. Comp. Math. Appl. Mech. Eng. (to appear).
Strang, G., Approximation in the finite element method. Num. Math. 19, 81–98 (1972). For evolution problems, we mention
Douglas, J., Dupont, T., Galerkin methods for parabolic equations. SIAM J. Num. Anal. 7, 4, 575–626 (1970).
Dupont, T., estimates for Galerkin methods for second order hyperbolic equations (to appear).
Raviart, P. A., The use of numerical integration in finite element methods for solving parabolic equations, Conference on Num. Anal., Royal Irish Academy, Dublin, 1972.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer-Verlag, Berlin · Heidelberg
About this chapter
Cite this chapter
Lions, J.L., Magenes, E. (1973). Evolution Equations of the Second Order in t and of Schroedinger Type. In: Non-Homogeneous Boundary Value Problems and Applications. Die Grundlehren der mathematischen Wissenschaften, vol 183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65393-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-65393-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65395-7
Online ISBN: 978-3-642-65393-3
eBook Packages: Springer Book Archive