PROBLEME AUX LIMITES POUR UNE CLASSE D’EQUATIONS AUX DERIVEES PARTIELLES DU TROISIEME ORDRE
Keywords:
estimation a priori, solution forteAbstract
Dans cet article on utilise la méthode des inégalités énergétiques, dite aussi méthode des estimations a priori, pour démontrer l’existence et l’unicité de la solution forte d’un problème aux limites avec des conditions locales pour une équation aux dérivées partielles du troisième ordre.Downloads
References
- Dainyak V.V. and Korzyuk V.I., "A Dirichlet-type problem for a third order linear differential equation", Diff. Equa., Vol.23, N°5, (1987), pp.598-602.
- Tsyvis N.V. and Yurchuk N.I., "A three-point boundary problem for third-order differential operational equations", Diff. Equa., Vol.23, N°5, (1987), pp.606-609.
- Gavrilova N.V. and Yurchuk N.I.: ”Cauchy problem for Euler-Poisson-Darboux differential operational equations”, Diff. Equa., Vol.17, N°5, (1981), pp.516-520.
- Yurchuk N.I., "Boundary-value problems for equations whose principal part contains operators of the form ", Diff. Equa., Vol.10, N°4, (1974), pp.589-592.
- Yurchuk N.I., "Boundary-value problems for equations involving operators of the form ", Diff. Equa., Vol.10, N°5, (1974), pp.735-737.
- Yurchuk N.I., "A priori estimates of solutions of Boundary-value problems for certain differential equations", Diff. Equa., Vol.12, N°4, (1976), pp.512-518.
- Yurchuk N.I., "Boundary-value problems for differential equations with operation-valued coefficients depending on a parameter", Diff. Equa., Vol.12, N°9, (1976), pp.1157-1168.
- Yurchuk N.I., "Solvability of boundary-value problems for certain differential equations", Diff. Equa., Vol.13, N°4, (1977), pp.423-429.
- Yurchuk N.I., "Boundary-value problems for differential equations with operator-valued coefficients depending on a parameter", Diff. Equa., Vol.14, N°5, (1978), pp.609-617.
- Yurchuk N.I., "The energy inequality method in the investigation of certain degenerate linear operational differential equations", Diff. Equa., Vol.14, N°12, (1978), pp.1558-1567.
- Yurchuk N.I., "Mixed problems for parabolic equations of variable order", Soviet. Math. Dokl., Vol.26, N°1, (1982), pp.39-41.
- Yurchuk N.I., "Mixed problems for linearized Korteweg–de-Vries equations degenerating in time into parabolic equations", Soviet. Math. Dokl., Vol.33, N°2, (1986), pp.435-437.
- Agmon S., "Lectures on elliptic boundary- value problems", D.Van-Nostrand Company (1965).
- Petrovskey I.G., "Uber das Cauchyshe problem fûr ein system linearren partialler differential glienchungen in gebeit der nichtanalytischen funktioen", Bull. D’êtat. Moscow 1A N°7, (1938), pp.1-17.
- Leray J., "Hyperbolic differential equations", Princeton (1952).
- Gårding L., "Cauchy’s problem for hyperbolic equations", Univ. of Chicago (1958).
- Courant and Hilbert, "Methods of mathematical physics", ChVI. Vol. II.
- Brezis H., Opérateurs maximaux monotones", Noth-Holland (1973).
- Tanabe H., "Equation of evolution” (Ch2, pp.19-88) Monographs and studies in Mathematics 6 Pitman Pub. Lin. Transl (1975).
- Lusternik L. and Sobolev V., "Elements of functional analysis", Hindustan. Pub. corporation (India) (1974).
- Trenoguine V., "Analyse fonctionnelle", Ed. Mir. (1981).
- Lions J.L., "Espaces d’interpolation et domaines des puissances fractionnaires d’opérateurs", J. Math. Soc. Japan, Vol.14, N°2, (1962), pp.233-241.
- Kato T., "Fractional powers of dissipative operators", J. Math. Soc. Japan, Vol.13, N°3, (1961), pp.246-274.
- Kato T., "Fractional powers of dissipative operators, II", J. Math. Soc. Japan, Vol.14, N°2, (1962), pp.242-248.
- Krasnoselskii M.A., "Integral operators in spaces of summable functions", Nauka. Moscow, (1966), English transl. Noordhoff, (1975).
- Krein S.G., "Linear differential equation in Banach space", Moscow-Nauka (1967), A. M. S 1972.