On unstable sets of evolution equations in the neighborhood of critical points of a stationary curve

Equations of the form $\partial_t u=A(u,\lambda)$ are considered, for example, parabolic and hyperbolic equations. It is proved that the change of the local unstable invariant manifolds of such equations is determined by the form of the stationary curve $(u,\lambda)=(U(\xi),\Lambda(\xi))$, $A(u,\lambda)=0$.
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