Existence of multidimensional phase transitions in a non-isothermal van der Waals fluid

In this paper, we prove the existence of multidimensional subsonic phase transitions in a non-isothermal van der Waals fluid. The argument is based on the result of the existence of travelling waves given in [S.-Y. Zhang, Existence of travelling waves in non-isothermal phase dynamics, J. Hyperbolic Differ. Equ. 4 (3) (2007) 391–400] and the result of multidimensional stability given in [S.-Y. Zhang, Stability of multidimensional subsonic phase transition in a non-isothermal van der Waals fluid, Preprint]. An iteration technique [A. Majda, The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 281 (1983) 1–93] is applied to achieve the result.