Abstract:
This article investigates the boundary value problem for the quasilinear parabolic equations. The existence of solutions in Sobolev's spaces $W_p^{2m,1}$ is proved, as well as the convergent of the approximate solutions, built according to Galerkin's method, to the exact solution with respect to the norm of the space $ W_2^{2m,1}$. The estimates of the convergence for some types of nonlinean are obtained.
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