On the unbounded solutions for parabolic differential-functional Cauchy problem

• Autorzy: Topolski K.
• Języki publikacji: EN

Abstrakty

EN

We consider the initial value problem for second order differential–func- tional equation. Functional dependence on an unknown function is of the Hale type. We prove the existence theorem for unbounded classical solution. Our formulation admits a large group of nonlocal problems. We put particular stress on “retarded and deviated” argument as it seems to be the most difficult.

Słowa kluczowe

EN

parabolic equation; Cauchy problem; differential-functional equation

PL

równanie paraboliczne; zagadnienie Cauchy'ego; równanie różniczkowo-funkcjonalne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 1
• Strony: 151--160
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Topolski K.

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

Bibliografia

• [1] J. K. Hale, S. M. V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag New York 1993.
• [2] 0. A. Ladyzhenskaya, V. A. Solonikov, N. N. Uralceva, Linear and Quasilinear Equation of Parabolic Type, Nauka, Moskva, 1967 [Russian]. (Translation of Mathematical Monographs, Vol. 23, Am.Math.Soc., Providence, R.I., 1968.)
• [3] H. Leszczyński, On a nonlinear heat equation with functional dependence, Appl. Anal. 74 (2000), 233-251.
• [4] K. A. Topolski, Parabolic differential-functional inequalities in a viscosity sense, Ann. Polon. Math. 68 (1998), 17-25.
• [5] K. A. Topolski, On the classical solutions for parabolic differential-functional Cauchy problem, Comment. Math. 44, no 2 (2004), 217-226.