Systems of conservation laws, qualitative properties and singularities of generalized solutions, variational representation of solutions. Systems of equations of multicomponent filtration type.
Main publications:
Yu. G. Rykov, “O kharaktere rasprostraneniya vozmuschenii dlya suschestvenno neavtonomnykh kvazilineinykh uravnenii pervogo poryadka.”, Trudy seminara im. I. G. Petrovskogo, 17, 1994, 89–117
W. E., Yu. G. Rykov, Ya. G. Sinai, “Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics”, Comm. Math. Phys., 177 (1996), 349–380
Yu. G. Rykov, “Discontinuous solutions of some strongly degenerate parabolic equations.”, Russian Journal of Mathematical Physics, 7:3 (2000), 341–356
Yu. G. Rykov, “On the non-hamiltonian character of shocks in 2-D pressureless gas.”, Bolletino dell U.M.I. Sezione B, 5-B (2002), 55–78
A. I. Aptekarev, Yu. G. Rykov, “On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory”, Russian Journal of Math. Phys., 13:1 (2006), 4–12