TY  - JOUR
AU  - Yaremenko, Mykola 
PY  - 2020
TI  - The Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential Equations
JF  - Journal of Mathematics and Statistics
VL  - 16
IS  - 1
DO  - 10.3844/jmssp.2020.76.89
UR  - https://thescipub.com/abstract/jmssp.2020.76.89
AB  - 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.