Pavel Holba
Conservation laws for Extended Generalized Cahn–Hilliard–Kuramoto–Sivashinsky Equation in Any Dimension
We present a complete characterization of nontrivial local conservation laws for the extended generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation in any space dimension. This equation naturally generalizes the well-known and widely used Cahn–Hilliard and Kuramoto–Sivashinsky equations, which have manifold applications in chemistry, physics, and biology. In particular, we demonstrate that any nontrivial local conservation law of any order for the equation under study is equivalent to a conservation law whose density is linear in the dependent variable with the coefficient at the dependent variable depending only on the independent variables.
For further details please see the paper P. Holba, Conservation laws for extended generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation in any dimension. J Math Chem (2025). https://doi.org/10.1007/s10910-025-01717-w.
