Uniqueness theorem for parabolic Cauchy problem

Abstract

We proved uniqueness of a classical solution to the Cauchy problem in Tikhonov classes for Petrovskii second order parabolic systems with bounded, continuous and Dini-continuous with respect to the space variable coefficients.

Keywords:

• Parabolic systems
• Cauchy problem
• uniqueness theorem

AMS Subject Classifications:

• 35K45
• 35A02
• 35A09

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The results of the work are obtained in the framework of the state order of the Ministry of Education and Science of the Russian Federation [project number 1.756.2014/K].