Existence of Global Attractors for a Semilinear Wave Equation with Nonlinear Boundary Dissipation and Nonlinear Interior and Boundary Sources with Critical Exponents

摘要

In this paper we study a long-time dynamics for a nonlinearly forced 3-D wave equation subject to nonlinear boundary dissipation. Nonlinear forces are of critical exponent and supported both in the interior and on the boundary. While global attractors for wave equations with geometrically restricted damping and critical interior forcing have been known, a treatment of critical nonlinearity supported on the boundary, within the context of theory of global attractors, was an open question. The method devised for solution to the problem relies on "hidden regularity" established for Neumann hyperbolic problems and new tangential-boundary estimates which are also of independent interest.