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Notes on infinite-dimensional nonlinear parabolic equations

Authors:

M N Feller

Institution:

(1) UkrNIMOD, Kiev

Abstract:

We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations

$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {\Delta _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,\Delta _L U\left( {t,x} \right)} \right),$

and

$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right), \Delta _L U\left( {t,x} \right)} \right)$

with the infinite-dimensional Laplacian Δ_L.

Keywords:

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