On wave equation: review and recent results
The first part of the article is devoted to a short review of some results on initial-boundary value problems for different kinds of nonlinear wave equations, pointing out authors own achievements. In the second part one remembers the definitions of variable-exponent Lebesgue and Sobolev spaces and shows the existence of a unique weak solution and a decay result to a specific IBV problem for the wave equation with nonlinear damping. Numerical applications for polynomial as well as exponential decay are discussed. Article ends with a blowup result to another IBV problem for a wave equation with nonlinear damping.
variable-exponent Lebesgue and Sobolev spaces
scientific article; zbMATH DE number 6879953
scientific article