Regularity of solutions of parabolic equations with coefficients depending on t and parameters

• Autorzy: T. Winiarska
• Języki publikacji: EN

Abstrakty

EN

The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem $du/dt + A_h(t)u(t) = f_h(t)$, $u(0)=u_h^0$. The continuity of u with respect to both h and t has been considered in [6].

Kategorie tematyczne

• 35B30: Dependence of solutions on initial and boundary data, parameters

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 3
• Strony: 311-317

Daty

wydano

1992

otrzymano

1991-06-20

Twórcy

autor

T. Winiarska

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

Bibliografia

• [1] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, 1981.
• [2] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966.
• [3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
• [4] P. E. Sobolevskiĭ, On equations of parabolic type in a Banach space, Trudy Moskov. Mat. Obshch. 10 (1986), 297-350 (in Russian).
• [5] H. Tanabe, Equations of Evolution, Pitman, 1979.
• [6] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339.
• [7] T. Winiarska, Evolution equation with parameter, Univ. Iag. Acta Math. 28 (1987), 219-227.
• [8] T. Winiarska, Differential Equations with Parameters, Monograph 68, Technical University of Cracow, 1988.
• [9] K. Yosida, Functional Analysis, Springer, 1980.