We consider local properties of zero sets dependent of time variable of analytic solutions of linear second order parabolic equations with two spatial variables. Our aim is to give several necessary conditions for the zero set at the present to be homeomorphic to those at the recent past and at the recent future.
Kinji WATANABE. "Zero sets of solutions of second order parabolic equations with two spatial variables." J. Math. Soc. Japan 57 (1) 127 - 136, January, 2005. https://doi.org/10.2969/jmsj/1160745817