Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.
@article{bwmeta1.element.doi-10_1515_math-2016-0025,
author = {Huashui Zhan and Shuping Chen},
title = {The BV solution of the parabolic equation with degeneracy on the boundary},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {272-282},
zbl = {1346.35129},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0025}
}
Huashui Zhan; Shuping Chen. The BV solution of the parabolic equation with degeneracy on the boundary. Open Mathematics, Tome 14 (2016) pp. 272-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0025/