On the analytic continuation of solutions to nonlinear partial differential equations


AbstractWe consider the analytic continuation of solutions to the nonlinear partial differential equation ∂∂tmu=Ft,x,∂∂tj∂∂xαuj+|α|⩽mj⩽m−1 in the complex domain. Suppose a solution u(t,x) is known to be holomorphic in the domain {(t,x)∈C×Cn;|x|<R,0<|t|<r and |argt|<θ} for some positive numbers R,r and θ. Then we can show that if u(t,x) satisfies some growth condition as t approaches zero, it is possible to extend it as a holomorphic solution of this partial differential equation up to some neighborhood of the origin

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Last time updated on 6/5/2019

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