Approximation of a Cauchy problem solution for a parabolic equation with nonlinear potential
AbstractThe Cauchy problem for a quasilinear parabolic equation with local and nonlocal equation potential is considered. For equation of "reaction-diffusion" type with convex local potential the barrier functions, which are the upper and lower estimates of the solution of the Cauchy problem, are constructed. Method of construction of the mentioned barrier function is the composition of the two solutions of differential equations with nonlocal equations. For the equation with a nonlocal potential logistics properties, which are built in a similar way as the barrier function of the upper estimate, it is verified by computing experiment.
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