Wave equations with time-dependent dissipation. II: Effective dissipation (Q859518)

The article represents the second part of a series devoted to wave equation with dissipation, the first of which [J. Differ. Equations 222, No. 2, 487--514 (2006; Zbl 1090.35047)] dealt with non-effective dissipation. The author constructs structural representations of a solution to the Cauchy problem for the equation \(u_{tt}-\triangle u+b(t)u_{t}=0\) and gives \(L_{p}\)-\(L_{q}\) estimates of the solution in the case of a positive coefficient \(b(t)\) satisfying \(tb(t)\rightarrow +\infty \) if \(t\rightarrow +\infty .\)