In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g(t, ut) may be driven by a… Click to show full abstract
In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g(t, ut) may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback D-attractor in $${C_{H_0^1\left( \Omega \right)}} \times {C_{{L^2}\left( \Omega \right)}}$$CH01(Ω)×CL2(Ω) by constructing the energy functional and combining with the idea of the contractive function.
               
Click one of the above tabs to view related content.