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@article{78146,
author = {Holba, Pavel},
article_location = {Hoboken (USA)},
article_number = {1},
doi = {http://dx.doi.org/10.1111/sapm.12576},
keywords = {Cahn-Hilliard equation; conservation laws; Kuramoto-Sivashinsky equation},
language = {eng},
issn = {0022-2526},
journal = {Studies in Applied Mathematics},
title = {Complete classification of local conservation laws for generalized Cahn-Hilliard-Kuramoto-Sivashinsky equation},
url = {https://onlinelibrary.wiley.com/doi/10.1111/sapm.12576},
volume = {151},
year = {2023}
}
TY - JOUR
ID - 78146
AU - Holba, Pavel
PY - 2023
TI - Complete classification of local conservation laws for generalized Cahn-Hilliard-Kuramoto-Sivashinsky equation
JF - Studies in Applied Mathematics
VL - 151
IS - 1
SP - 171-182
EP - 171-182
PB - WILEY
SN - 00222526
KW - Cahn-Hilliard equation
KW - conservation laws
KW - Kuramoto-Sivashinsky equation
UR - https://onlinelibrary.wiley.com/doi/10.1111/sapm.12576
N2 - In this paper, we consider nonlinear multidimensional Cahn-Hilliard and Kuramoto-Sivashinsky equations that have many important applications in physics and chemistry, and a certain natural generalization of these two equations to which we refer to as the generalized Cahn-Hilliard-Kuramoto-Sivashinsky equation. For an arbitrary number of spatial independent variables, we present a complete list of cases when the latter equation admits nontrivial local conservation laws of any order, and for each of those cases, we give an explicit form of all the local conservation laws of all orders modulo trivial ones admitted by the equation under study. In particular, we show that the original Kuramoto-Sivashinsky equation admits no nontrivial local conservation laws, and find all nontrivial local conservation laws for the Cahn-Hilliard equation.
ER -
HOLBA, Pavel. Complete classification of local conservation laws for generalized Cahn-Hilliard-Kuramoto-Sivashinsky equation. \textit{Studies in Applied Mathematics}. Hoboken (USA): WILEY, 2023, vol.~151, No~1, p.~171-182. ISSN~0022-2526. Available from: https://dx.doi.org/10.1111/sapm.12576.
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