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ISSN: 1558-6359 (Online)
Research Article Open Access

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

Mykola Yaremenko1
  • 1 Partial Differential Equation, Ukraine

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 of Mathematics and Statistics
Volume 16 No. 1, 2020, 76-89

DOI: https://doi.org/10.3844/jmssp.2020.76.89

Submitted On: 1 April 2020 Published On: 2 June 2020

How to Cite: Yaremenko, M. (2020). The Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential Equations. Journal of Mathematics and Statistics, 16(1), 76-89. https://doi.org/10.3844/jmssp.2020.76.89

Open AccessCopyright: © 2020 Mykola Yaremenko. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Quasi-Linear Partial Differential Equations
  • Nonlinear Partial Differential Equations
  • Parabolic
  • Nonlinear Operator
  • Weak Solution
  • A Priori Estimations