A Method for the Construction of Reflection Laws for a Parabolic Equation

C. Denson Hill
1968 Transactions of the American Mathematical Society  
In this paper we consider the parabolic equation (1.1) uz = auí(+2buf" + cum + duí + euv+fu with b2 -ac<0 whose coefficients are holomorphic functions of £, r¡ and t. We present a general method for the construction of explicit reflection formulae (analogous to the classical Schwarz reflection principle for harmonic functions) for solutions of (1.1) which vanish along a noncharacteristic analytic surface. These formulae (cf. (8.3) and (8.7) ) have a domain of dependence consisting, in
doi:10.2307/1994984 fatcat:4lim5ohuejdwfnbss2v3u6khf4