On the Analyticity of Solutions of First-Order Nonlinear PDE
On the Analyticity of Solutions of First-Order Nonlinear PDE
Let $(x,t) \in {R^m} \times R$ and $u \in {C^2} ({R^m} \times R)$. We discuss local and microlocal analyticity for solutions $u$ to the nonlinear equation \[ {u_t}= f(x,t,u,{u_x})\] . Here $f(x,t,{\zeta _0},\zeta )$ is complex valued and analytic in all arguments. We also assume $f$ to be holomorphic in …