Local and global existence for evolution p-Laplacian equation with time-dependent source

Abstract

We study the Cauchy problem for the evolution p-Laplacian equation with time-dependent source on the assumption that the initial values are taken in the sense of . Here we obtain the local existence, global existence and nonexistence of solutions. Particularly, the limiting case is also studied.

Keywords:

• evolution p-laplacian equation
• strongly nonlinear source
• local existence
• global existence and nonexistence

AMS Subject Classifications::

• 35K15
• 35K55

Acknowledgements

The author thanks the referees for a careful reading of the original manuscript and for giving revision of the proof of Theorem 1.5 which makes the proof much easier and readable. This study is supported by a Doctoral Foundation of Henan Polytechnic University (No. B2011-049).