A maximum principle for a loaded hyperbolic-parabolic equation

We prove the maximum principle for a loaded equation of hyperbolic-parabolic type with variable coefficients. The characteristic load term is given on the degenerate line. The obtained results generalize the maximum principle for hyperbolic-parabolic equations provided in T. D. Dzhuraev's monograph, and in the hyperbolic domain the well-known Agmon–Nirenberg–Protter principle.