Weak solutions for a class of metaparabolic equations

Abstract

In this article, the author investigates the initial boundary value problem for a class of metaparabolic equations, which arise in the dynamics of viscous first-order phase transitions in cooling binary solutions. By using the method of continuity, we establish the existence of weak solutions.

Keywords:

• metaparabolic equation
• weak solutions
• existence

AMS Subject classifications:

• 35D05
• 35G25
• 35G30

Acknowledgement

The author would like to thank Prof. Yin Jingxue for the discussion and the referee's valuable suggestions for the revision and improvement of the manuscript.