The uniqueness in Cauchy problems for linear partial differential equations with C~∞ coefficients is of quite complication. In 1974, M. Strauss and F. Treves proved uniqueness in the Cauchy problem u_t+ib(x, t)u_x+c(x,t)u=0 and u(x, 0)=0, where t b(0,t) vanishes of finite order at t=0. In this paper, by using the technique of pseudo-differential operators, we give a general result on the uniqueness in Cauchy problems for systems of equations of order m≥1 with two independent variables.
ON THE UNIQUENESS IN CAUCHY PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS. Acta Mathematica Sinica, Chinese Series, 1979, 22(5): 569-578 https://doi.org/10.12386/A1979sxxb0052