Lineer ve lineer olmayan sönüm terimli dalga denklemlerinin enerji azalımı ve asimtotik davranışı

In this thesis we survey energy decay and asymptotic behavior ofsolutions to the Cauchy problems for the linear and nonlinear waveequations with dissipative terms. The thesis consists of four chapters.In the ? rst chapter, necessary de ? nitions and theorems are given.In the second chapter, it is shown that the solution of the Cauchyproblem to the linear wave equation with damping with variablecoecoefficient decays to zeropolynomially as t tends to infinity. In the third chapter, it isproved that the solution to the Cauchy problem for the nonlineardissipative wave equation decays to zero as t tends to infinity. Inthe last chapter, a short discussion of the advantages of thestrengthened multipliers method used in the thesisis given.