A new kind of the solution of degenerate parabolic equation with unbounded convection term

Huashui Zhan

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page Article ID 22, 21 p., electronic only-Article ID 22, 21 p., electronic only
  • ISSN: 2391-5455

Abstract

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A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.

How to cite

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Huashui Zhan. "A new kind of the solution of degenerate parabolic equation with unbounded convection term." Open Mathematics 13.1 (2015): Article ID 22, 21 p., electronic only-Article ID 22, 21 p., electronic only. <http://eudml.org/doc/270899>.

@article{HuashuiZhan2015,
abstract = {A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = \{Ei\} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.},
author = {Huashui Zhan},
journal = {Open Mathematics},
keywords = {Cauchy problem; Degenerate parabolic equation; Entropy solution; Unbounded convection term; anisotropic degenerate parabolic equation; boundary condition; entropy solution},
language = {eng},
number = {1},
pages = {Article ID 22, 21 p., electronic only-Article ID 22, 21 p., electronic only},
title = {A new kind of the solution of degenerate parabolic equation with unbounded convection term},
url = {http://eudml.org/doc/270899},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Huashui Zhan
TI - A new kind of the solution of degenerate parabolic equation with unbounded convection term
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - Article ID 22, 21 p., electronic only
EP - Article ID 22, 21 p., electronic only
AB - A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.
LA - eng
KW - Cauchy problem; Degenerate parabolic equation; Entropy solution; Unbounded convection term; anisotropic degenerate parabolic equation; boundary condition; entropy solution
UR - http://eudml.org/doc/270899
ER -

References

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