On internal elastic membrane with strong damping.
Under some assumptions on \(M,A,F\) the authors prove existence and uniqueness of weak and strong solutions of the initial problem to the equation \(u_{tt}+M(\| u(t)\| ^2)Au(t)+Fu(t)+Au'(t)=0\) in a real Hilbert space, where \(t\in (0,T)\), \(M\) is degenerate real function and \(A,F\) are operators. Furthermore, energy decay \(E(t)\leq C(1+t)^{-(1+1/s)}\) of the initial Dirichlet boundary value problem to the equation \(u_{tt}-\| u(t)\| ^{2s}\Delta u+g(u)-\Delta u_t=0\) is established.
scientific article; zbMATH DE number 6033864