A complete characterization of extinction versus positivity of solutions to a parabolic problem of p-Laplacian type in graphs

作者：Chung Soon Yeong; Park Jea Hyun^*

来源：Journal of Mathematical Analysis and Applications, 2017, 452(1): 226-245.

DOI：10.1016/j.jmaa.2017.03.010

• Extinction
• Asymptotic behavior
• Nonlinear absorption
• Extinction time

This work is concerned with the extinction and positivity properties of solutions to the discrete p-Laplacian parabolic equation u(t) = Delta(p,omega) u - f (u), p > 1 with a nonlinear absorption on a weighted graph. We provide a complete characterization for f to see when we have an extinctive solution or a positive solution. In addition, the extinction time is estimated for the extinctive solutions, and the decay rate is given to the positive solutions. Finally, we give several numerical examples which illustrate the main results.

• 出版日期2017-8-1