PETROVSKII 286 



Prizes. He is a member of the Soviet Committee on Defense 

 of Peace. 



The work of Petrovskii is concerned with the theory of 

 partial differential equations, algebraic geometry, qualitative 

 theory of differential equations, and theory of probability. He 

 studied the various classes of elliptical systems (1937), studied 

 problems with initial conditions for parabolic and hyperbolic 

 systems of equations (1936); investigated the dependence of so- 

 lutions on initial conditions; indicated for hyperbolic equations 

 with constant coefficients the necessary and adequate conditions 

 of existence of lacunae, that is, those regions in the base of the 

 characteristic cone, the initial conditions of which do not influ- 

 ence the significance of the solution at the cone vortex (1944). 

 For his studies on the theory of partial differential equations 

 Petrovskii was awarded, in 1946, a Stalin Prize. Petrovskii 

 has also solved the first boundary -value problem for the 

 equation of heat conductivity using the most general assumptions 

 concerning the boundary of the domain (1935), gave the solution 

 of the Dirichlet problem for the Laplace equation by the method 

 of finite differences in an n-measured domain (1941), studied 

 the behavior of integral curves for the system of ordinary 

 differential equations in the vicinity of a singular point (1934), 

 and obtained a series of results in the theory of probability. In 

 the area of algebraic geometry, Petrovskii studied the distri- 

 bution of ovals of the algebraic curve of the sixth order (1935). 

 The method allowed solution of a more general problem which 

 gives the distribution of ovals of an algebraic curve of any 

 order, and establishes the topological properties of algebraic 

 surfaces and algebraic manifolds of any number of dimensions 

 (1949). Petrovskii, together with E. M. Landis, obtained (1955- 

 57) evaluations of the number of limiting cycles in the ordinary 

 differential equations, the right part of which is a ratio of two 

 polynomials of the nth power; in the case where n = 2, their 

 evaluation is exact. He is the author of textbooks, Lectures on 

 the Theory of Ordinary Differential Equations (1939), Lectures 

 on the Theory of Integral Equations (1948), Lectures on 

 Equations with Partial Derivatives (1950), which were pub- 

 lished many times in the U.S.S.R. and translated to foreign 

 languages (Stalin Prize 1952). 



In 1961 PetrovsKii was awarded the Order of Lenin. In 

 March 1962, he was elected delegate from R.S. F.S.R. to the 

 Supreme Soviet. 



As of 1961, Petrovskii was a Member of the Presidium of 

 the U.S.S.R. Academy of Sciences. 



