Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case
Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case
We study the Cauchy problem for the quasilinear wave equation $ \partial^2 _t u = u^{2a} \partial^2_x u + F(u) u_x $ with $a \geq 0$ and show a result for the local in time existence under new conditions. In the previous results, it is assumed that $u(0,x) \geq c_0>0$ …