On the quasilinear Cauchy problem for a hyperbolic functional differential equation

• Autorzy: Puźniakowska-Gałuch E.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.6.915

• Języki publikacji: EN

Abstrakty

EN

The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.

Słowa kluczowe

EN

functional differential equations; Haar pyramid; differentiability of solutions; Fredholm type of equation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 6
• Strony: 915--933
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Puźniakowska-Gałuch E.

• University of Gdańsk Institute of Mathematics Wit Stwosz Street 57 80-952 Gdańsk, Poland

Bibliografia

• [1] V.E. Abolina, A.D. Myshkis, Mixed problem for semilinear hyperbolic systems on the plane, Mat. Sb. 50 (1960), 423-442 [in Russian].
• [2] P. Bassanini, M.C. Salvadori, (In problema ai limiti per sistemi integrodifferenziali nonlineari di tipo iperbolico, Boll. Un. Mat. Ital. B 5 (1981) 13, 785-798.
• [3] P. Brandi, R. Ceppitelli, Existence, uniqueness and continuous dependence for hereditary nonlinear functional partial differential equation of the first order, Ann. Polon. Math. 47 (1986) 2, 121-136.
• [4] P. Brandi, A. Salvadori, Z. Kamont, Existence of generalized solutions of hyperbolic functional differential equations, Nonlinear Anal. 50 (2002) 7, 919-940.
• [5] W. Czernous, Semilinear hyperbolic functional differential problem on a cylindrical domain, Bull. Belg. Math. Soc. Simon Stevin 19 (2012) 1, 1-17.
• [6] T. Człapiński, Z. Kamont, Generalized solutions of local initial problems for quasi-linear hyperbolic functional-differential systems, Studia Sci. Math. Hungar. 35 (1999) 1-2, 185-206.
• [7] W. Eichhorn, W. Gleissner, On a functional differential equation arising in the theory of the distribution of wealth, Aequationes Math. 28 (1985), 190-198.
• [8] M. El Doma, Analysis of nonlinear integro-differential equations arising in the age-dependent epidemic models, Nonlinear Anal. 11 (1987), 913-937.
• [9] J.H. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, Berlin, 1993.
• [10] D. Jaruszewska-Walczak, Existence of solutions of first order partial differential-functio­nal equations, Boll. Un. Mat. Ital. B 4 (1990) 1, 57-82.
• [11] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Mathematics and its Applications, vol. 486, Kulwer Academic Publishers, Dordrecht, 1999.
• [12] E. Puźniakowska-Gałuch, Generalized Cauchy problems for hyperbolic functional differential systems, Ann. Polon. Math. 110 (2014), 33-53.
• [13] E. Puźniakowska-Gałuch, Initial problems for hyperbolic functional differential systems, Georgian Math. J. 20 (2013) 2, 357-376.
• [14] E. Puźniakowska-Gałuch, Differentiability with respect to initial functions for partial functional differential equations, Univ. lag. Acta Math. 48 (2010), 111-131.
• [15] E. Puźniakowska-Gałuch, On the local Cauchy problem for first order partial differential functional equations, Ann. Polon. Math. 98 (2010), 39-61.
• [16] E. Puźniakowska, Classical solutions of quasilinear functional differential systems on the Haar pyramid, Diff. Equat. and Appl. 1 (2009) 2, 179-197.
• [17] E. Sinestrari, G.F. Webb, Nonlinear hyperbolic systems with nonlocal boundary conditions, J. Math. Anal. Appl. 121 (1987), 449-464.
• [18] J. Szarski, On integro-differential equations, Ann. Polon. Math. 14 (1964), 321-333.
• [19] J. Turo, A boundary value problem for hyperbolic systems of differential-functional equations, Nonlinear Anal. 13 (1989) 1, 7-18.
• [20] J. Turo, Local generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in two independent variables, Ann. Polon. Math. 49 (1989) 3, 259-278.
• [21] J. Wu, Theory and Applications of Partial Functional-Differential Equations, Applied Mathematical Sciences, 119, Springer-Verlag, New York, 1996.