Existence and uniqueness of classical solutions to semilinear Darboux problems together with nonstandard conditions with integrals

• Autorzy: Byszewski L.
• Języki publikacji: EN

Abstrakty

EN

The existence and uniqueness of classical solutions to semilinear hyperbolic differential Darboux problems for the equation [formula] together with nonstandard conditions with integrals in bounded and unbounded domains are studied.

Słowa kluczowe

EN

hyperbolic differential problem; Darboux problem; semilinear problem; nonstandard conditions with integrals; existence and uniqueness of a classical solution; Banach contraction theorem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2003
• Tom: [Z] 43(2)
• Strony: 169--183
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Byszewski L.

• Cracow University of Technology, Institute of Mathematics, Warszawska 24, 31-155 Cracow, Poland

Bibliografia

• [1] J. Brandys and L. Byszewski, Uniqueness of solutions to inverse parabolic problems, Comment. Math. Prace Matem. 42 (2002), 17-30.
• [2] L. Byszewski, Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals, Journal of Applied Mathematics and Stochastic Analysis 3.5 (1990), 65-80.
• [3] L. Byszewski, Differential and Functional-Differential Problems with Nonlocal Conditions, Cracow University of Technology Monographs. Monograph 184, Cracow 1995 (in Polish).
• [4] J. Chabrowski, On the non-local problem with a functional for parabolic equation, Funkcialaj Ekvacioj 27 (1984), 101-123.
• [5] H. Chi, H. Poorkarimi, J. Wiener and S. M. Shah, On the exponential growth of solutions to nonlinear hyperbolic equations, Intern. Jour. Math. and Math. Sciences 12.3 (1989), 539-545.
• [6] M. Krzyżański, Partial Differential Eąuations of Second Order, Vol. 2, PWN (Polish Scientific Publishers), Warsaw 1971.