Geodesic
On the method of Galerkin for the quasilinear parabolic equations in noncylindric domain
Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 1, pp. 3-17

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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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     author = {P. V. Vinogradova and A. G. Zarubin},
     title = {On the method of {Galerkin} for the quasilinear parabolic equations in noncylindric domain},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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P. V. Vinogradova; A. G. Zarubin. On the method of Galerkin for the quasilinear parabolic equations in noncylindric domain. Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/DVMG_2002_3_1_a0/