Information on the thesis

The thesis for obtaining the Candidate of Physical and Mathematical Sciences
degree on the speciality 01.01.02 — Differential equations. — Ivan Franko National
University of Lviv, Lviv, 2015.
In the thesis a group classification of a certain class of non-linear five-dimensional
D’Alembert equations in the space M(1, 4)×R(u) has been performed. Non-equivalent
functional bases of the first-order differential invariants for non-conjugate subgoups
of the Poincar´e group P(1, 4) have been constructed. A criterion of equivalence for
functional bases of the first-order differential invariants for non-conjugate subgoups of
the Poincar´e group P(1, 4) has been formulated and proven. For some P(1, 4)-invariant
five-dimensional D’Alembert equations, the symmetry reduction has been performed
and some classes of invariant solutions have been constructed.
Key words: group classification of differential equations, non-conjugate subgroups,
non-equivalent functional bases of differential invariants, symmetry reduction, invari-
ant solutions.