Optimal decay rate of the energy for wave equations with critical potential
The authors study the long time behaviour of the solutions of the wave equation with a variable damping term. They are focused to the Cauchy problem for the case of potentials with critical decay. Their solution manifests a new threshold effect with respect to the size of the coefficient in the variable damping term. In additon, they obtain similar results in low dimensions and they have presented the estimates in the two dimensional case. Moreover, they determined that the decay estimate of the associated parabolic problem when the size of the coefficient in the variable damping term is much larger than 3.
scientific article; zbMATH DE number 6152432
scientific article