Hyperbolic equations in uniform spaces

• Autorzy: Cholewa J. W. , Dlotko T.
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of R^n. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space H[...]^R^n) x L[...](R^n). Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.

Słowa kluczowe

EN

wave equation; uniform spaces; dissipativeness; global attractor

PL

równanie falowe; przestrzeń jednostajna; atraktor globalny

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 249--263
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Cholewa J. W.

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

Dlotko T.

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [A-C-D-RB] J. Arrieta, J. W. Cholewa, T. Dlotko and A. Rodriguez-Bernal, Linear parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci. 14 (2004), 253-293.
• [CA-DL] A. N. Carvalho and T. Dlotko, Partly dissipative systems in uniformly local spaces, Colloq. Math. 100 (2004), 221-242.
• [C-D 1] J. W. Cholewa and T. Dlotko, Global Attractors in Abstract Parabolic Problems, Cambridge Univ. Press, Cambridge, 2000.
• [C-D 2] -, -, Cauchy problem with subcritical nonlinearity, J. Math. Anal. Appl. 210 (1997), 531-548.
• [F] E. Feireisl, Bounded, locally compact global attractors for semilinear damped wave equations in Rn, Differential Integral Equations 9 (1996), 1147-1156.
• [H] J. K. Hale, Asymptotic Behavior of Dissipative Systems, AMS, Providence, RI, 1988.
• [K] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rat. Mech. Anal. 58 (1975), 181-205.
• [M] A. Mielke, The complex Ginzburg-Landau equation on large and unbounded domains: sharper bounds and attractors, Nonlinearity 10 (1997), 199-222.
• [M-S] A. Mielke and G. Schneider, Attractors for modulation equations on unbounded domain-|existence and comparison, Nonlinearity 8 (1995), 743-768.
• [P] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.
• [T] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1997.