On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions
An initial boundary value problem in a cylinder with mixed boundary conditions for the Kirchhoff type equation is considered. The author gives sufficient conditions under which the problem in question has a unique local weak solution. To obtain this result, a linear recurrent procedure and compactness arguments are exploited.
scientific article; zbMATH DE number 2173097
scientific article