The Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential Equations

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 u^z ∈ V_1,0², z = 1,2,..... to the Cauchy problems for the Equations (15) under the initial conditions u^z (0,x) = φ₀^z converges to the weak solution to the Cauchy problem for the Equation (1) under the initial condition u(0, x) = u₀ in V_1,0².