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Monotonic convergence of Newton's method for boundary value problems

I’m interested in solving nonlinear elliptic boundary value problems of the type $$ -a\Delta u + f(u) = 0, $$ $$ u|_\Gamma = u_0 $$ by Newton’s method when its convergence is global and monotonic. Cou …
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1 vote
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154 views

Lyapunov stability for nonlinear PDEs

Where can I find a theorem about Lyapunov stability for the equation in Hilbert space? $$ y' = Fy, $$ where $F : V \to V'$ is a nonlinear operator , $y' \in L^2(0,T,V')$, $V$ is a Hilbert space. Linea …
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