We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions.
Jin-soo Hwang. "Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation." Abstr. Appl. Anal. 2017 1 - 9, 2017. https://doi.org/10.1155/2017/4529847