A note on the global attractor for weakly damped wave equation

Abstract

a b s t r a c tIn this short note, we consider the long-time behavior for the solution of weakly damped wave equation with lower regular forcing. The existence of a global attractor is obtained. To verify asymptotic compactness of the semigroup, we present a new method about decomposition of the solution and apply the Strichartz estimate to the wave equation according to the recent progress. Moreover, translational regularity of the attractor is established.

A Finite Difference Method for Solving the Wave Equation with Fractional Damping

“…Recently, the study of damping effects has been a hot research topic because it appears in a variety of the dynamic processes of complex systems, including electromagnetic shunt [1], extensible beams [2], swelling porous elastic [3], vibration [4], and so on [5][6][7][8][9][10][11][12][13].…”

Strong attractors for weakly damped quintic wave equation in bounded domains

“…Working on the Shatah-Struwe solution semigroup arising from problem (1.1), Kalantarov et al [17] proved the existence and regularities of the compact global attractor in the case of sub-quintic and quintic growth rates of non-linearitiy f . Then, Liu et al [22,23,26] established the translational regular solution and studied the long-time behaviour of problem (1.1) with lower regular forcing (g ∈ H −1 ) and super-cubic non-linearity in both bounded and unbounded domains in R 3 . Recently, Savostianov and Zelik [31] studied the damped quintic wave equations with measure-driven and non-autonomous external forces in the 3-D perodic boundary conditions case.…”