Semilinear evolution equations of the parabolic type

• Autorzy: Jan Bochenek
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.

Słowa kluczowe

EN

classical solution; semilinear initial value problem; analytic semigroup; mild solution

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1999
• Tom: 72
• Numer: 3
• Strony: 197-206

Daty

wydano

1999

otrzymano

1997-10-09

poprawiono

1999-09-03

Twórcy

autor

Jan Bochenek

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

Bibliografia

• [1] P. Acquistapace and B. Terreni, On quasilinear parabolic systems, Math. Ann. 282 (1988), 315-335.
• [2] J. Bochenek, An abstract semilinear first order differential equation in the hyperbolic case, Ann. Polon. Math. 61 (1995), 13-23.
• [3] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer, Berlin, 1981.
• [4] T. Kato, Perturbation Theory of Linear Operators, Grundlehren Math. Wiss. 132, Springer, New York, 1980.
• [5] M. Kozak, An abstract nonlinear temporally inhomogeneous equation, Demonstratio Math. 23 (1990), 993-1003.
• [6] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
• [7] H. Tanabe, Equations of Evolution, Pitman, London, 1979.