Semináře

Program v akademickém roce 2019/2020

14. 11. 2019

Roman Popovych, D.Sc. (University of Vienna, Rakousko), Conditional symmetries of linear partial differential equations with two independent variables

Abstrakt:

We discuss reduction operators, i.e., operators of nonclassical (conditional) symmetry, of (1+1)-dimensional linear partial differential equations.

In particular, the reduction operators of (1+1)-dimensional second-order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. This “no-go” result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints.

The consideration of the above equations and of the (1+1)-dimensional linear rod equation is used to illustrate a new theorem on linear reduction operators of general linear partial differential equations.

Semináře se obvykle konají ve čtvrtek od 14.00 hod. v budově Matematického ústavu, Na Rybníčku 1 v Opavě, v místnosti R1. Všichni zájemci jsou srdečně zváni.