Notes on infinite-dimensional nonlinear parabolic equations - Feller, M. N. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {Δ _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,Δ _L U\left( {t,x} \right)} \right),$$ and $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right), Δ _L U\left( {t,x} \right)} \right)$$ with the infinite-dimensional Laplacian ΔL.