Abstract

We prove existence of the largest and the smallest entropy solutions to the Cauchy problem for a nonlinear degenerate anisotropic parabolic equation. Applying this result, we establish the comparison principle in the case when at least one of the initial functions is periodic. In the case when initial function vanishes at infinity (in the sense of strong average) we prove the long time decay of an entropy solution under exact nonlinearity-diffusivity condition.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call