Hyperbolic Equations in Uniform Spaces

• Autorzy: J. W. Cholewa , Tomasz Dlotko
• 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 $Ḣ¹_{lu}(ℝ ⁿ) × L̇²_{lu}(ℝ ⁿ)$. Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.

Kategorie tematyczne

• 35L15: Initial value problems for second-order hyperbolic equations
• 35B40: Asymptotic behavior of solutions
• 35B41: Attractors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 3
• Strony: 249-263

Daty

wydano

2004

Twórcy

autor

J. W. Cholewa

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

autor

Tomasz Dlotko

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

Identyfikatory

DOI

10.4064/ba52-3-5