In this paper we establish the blow up of solutions to the quasilinear wave equation with a nonlinear dissipative term utt-M(‖A^1/2U‖2^2)Au+|UT|^βut=|u|^pu x ∈Ω,t>0.
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local bound...Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.展开更多
文摘In this paper we establish the blow up of solutions to the quasilinear wave equation with a nonlinear dissipative term utt-M(‖A^1/2U‖2^2)Au+|UT|^βut=|u|^pu x ∈Ω,t>0.
文摘Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.
