Solution Representations for a Wave Equation with Weak Dissipation

الأصل · EN

We consider the Cauchy problem for the weakly dissipative wave equation v+μ1+tvₜ=0, x∈ⁿ, t≥ 0, parameterized by μ>0, and prove a representation theorem for its solution using the theory of special functions. This representation is used to obtain Lₚ--Lq estimates for the solution and for the energy operator corresponding to this Cauchy problem. Especially for the L₂ energy estimate we determine the part of the phase sp which is responsible for the decay rate. It will be shown that the situation d strongly on the value of μ and that μ=2 is critical.