Main area of ​​laboratory research is a mathematical analysis of the motion of continuous media with complex rheology. Among the models under consideration are the Navier-Stokes equations for the dynamics of a viscous heat-conducting gas; mathematical problems of the theory of nonlinear waves; equations of dynamics of non-Newtonian media; problems of contact discontinuities, cracks, and inclusions in the theory of elasticity; weak, strong, and entropy solutions of nonlinear and quasilinear parabolic and ultra-parabolic equations; stable solutions to mixed problems for autonomous hyperbolic systems; one-dimensional problems of calculus of variations with obstacles