Existence of solutions for wave-type hemivariational inequalities with noncoercive viscosity damping
A general hyperbolic hemivariational inequality is studied under the assumption that, in the term with the first order derivative of the unknown, the linear operator is not necessarily coercive. The nonlinear part of the equation is expressed by means of the generalized gradient of a locally Lipschitz function whose growth is strictly sublinear. The presence of the generalized gradient applied to the unknown determines for the problem the character of hemivariational inequality. The existence of solutions is proved on the basis of a special parabolic regularization technique and a suitable approximation method. Applications are given to treat various types of sine-Gordon equations.
scientific article; zbMATH DE number 1801638
scientific article