Nonlocal in time problems for evolution equations of second order

• Autorzy: Avalishvili G. A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, nonlocal in time problem for abstract evolution equation of second order is studied and theorem on existence and uniqueness of its solution is proved. Some applications of this theorem for hyperbolic partial differential equations and systems are considered and it is proved, that well-posedness of the mentioned problems depends on algebraic properties of ratios between the dimensions of the spatial boundary and the times appearing in the nonlocal in time initial conditions.

Słowa kluczowe

EN

second- order evolution equation; nonlocal in time conditions; algebraic numbers

PL

równanie ewolucji drugiego rzędu; nielokalne w czasie warunki; liczby algebraiczne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 2
• Strony: 245--259
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Avalishvili G. A.

• Institute of Applied Mathematics Tbilisi State University University Str. 2 380043 Tbilisi Georgia,

Bibliografia

• [1] Bourgin, D. G., Duffin, R., The Dirichlet problem for the vibrating string equation, Bull. Amer. Math. Soc. 45 (1939), 851-859.
• [2] Brezis, H., Analyse Fonctionelle, Masson, Paris, 1983.
• [3] Gelfond, A. O., Transcendental and Algebraic Numbers (in Russian), Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1952.
• [4] Gordeziani, D. G., On some initial conditions for parabolic equations, Reports of the Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics 4 (1989), 57-60.
• [5] Gordeziani, D. G., On one problem for the Navier-Stokes equation, Abstracts, Contin. Mech. Related Probl. Anal., Tbilisi (1991), 83.
• [6] Gordeziani, D.G., On solution of in time nonlocal problems for some equations of mathematical physics, ICM-94, Abstracts, Short Comm. (1994), 240.
• [7] Gordeziani, D. G., Grigalashvili, Z., Non-local problems in time for some equations of mathematical physics, Dokl. Semin. Inst. Prikl. Mat. im. I. N. Vekua 22 (1993), 108-114.
• [8] John, F., The Dirichlet problem for a hyperbolic equation, Amer. J. Math. 63 (1941), 141-154.
• [9] Schwartz, L., Théorie des distributions à valeurs vectorielles (I), Ann. Inst. Fourier 7 (1957), 1-142.