The main research areas of the laboratory are:

• theory of partial differential equations;

• group analysis of differential equations;

• preparing students for professional activities in the field of science and education.

The laboratory's activities are aimed at carrying out the following tasks:

• carrying out research work under the programs of the Ministry of Education and Science of the Russian Federation and other scientific programs of the Russian Federation, regional research programs, international scientific programs;

• development of scientific research at Elabuga Institute of KFU and Institute of Mathematics and Mechanics named after N.I. Lobachevsky, KFU;

• participation in professional training of students in the areas of work of Physics and Mathematics Faculty at Elabuga Institute of KFU and Institute of Mathematics and Mechanics named after N.I. Lobachevsky, KFU;

• increasing professional competence of the teaching staff of Elabuga Institute of    KFU;

• assistance in improving the qualifications of scientific and scientific-pedagogical personnel;

• introduction of the results obtained into the process of training students;

• involving students studying in the relevant specialties in research activities;

• providing research, consulting and educational services to organizations, specialists of educational institutions, students, schoolchildren.