@article {10.3844/jmssp.2020.76.89,
article_type = {journal},
title = {The Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential Equations},
author = {Yaremenko, Mykola},
volume = {16},
year = {2020},
month = {Jun},
pages = {76-89},
doi = {10.3844/jmssp.2020.76.89},
url = {https://thescipub.com/abstract/jmssp.2020.76.89},
abstract = {This article is dedicated to expanding our comprehension of the regularity of the solutions to the Cauchy problem for the quasilinear second-order parabolic partial differential equations under fair general conditions on the nonlinear perturbations. In this paper have been obtained that the sequence of the weak solutions uz ∈ V1,02, z = 1,2,..... to the Cauchy problems for the Equations (15) under the initial conditions uz (0,x) = φ0z converges to the weak solution to the Cauchy problem for the Equation (1) under the initial condition u(0, x) = u0 in V1,02.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}