Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity

Figure 1

The (𝑚,𝑛)-plane. The conservation laws are constrained to the region 𝑚≥0, 𝑛≥0. The special cases are the straight lines 𝑛+𝑚−1=0, 𝑛+𝑚−2=0, 𝑚=1, and 𝑛=𝑚−1.