On the nonlinear wave equation \(u_{tt}-B(\|u_{x} {\|}^{2})u_{xx}\) = \(f(x,t,u,u_{x},u_{t},{\|}u_{x}{\|}^{2})\) associated with the mixed homogeneous conditions
Using Galerkin method the authors prove the existence and uniqueness of the weak solution to the nonlinear wave equation \(u_{tt}-B(\|u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\|u_x\|^2)\) on \((0,1)\times (0,T)\) satisfying homogeneous mixed boundary conditions and some small initial data. Small perturbations of \(f\) are also discussed.
scientific article; zbMATH DE number 2001957
scientific article