Consider a system of PDEs

Suppose that is a positive solution to the system (with sufficient smooth property).

Find the two convex function and such that the functional

is decreasing in time.

It is enough to find and such that . We give a computation

The last relation suggests that if , then we get what we claim since .

Two approriate choices of mine:

and

[Update]

Since we want to use Csiszar-Kullback’s inequality, and should be

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## About baotangquoc

Lecturer
School of Applied Mathematics and Informatics
Hanoi University of Science and Technology
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