asymptotics; ordinary differential equations; partial differential equations; small parameter; hyperbolic systems of first-order PDE; shock waves; nonlinear differential equations.
Subject:
Area of a research - application of the theory of perturbation (method of a small parameter) to a Cauchy problem for a system of the quasilinear first order differential equations with small perturbations. The generalized solutions (solutions of Cauchy problem for system of conservation laws) are considered. Considered the discontinuous initial value problem (Riemann problem) for a hyperbolic system of two quasilinear equations with small perturbation. The asymptotics on a small parameter of an discontinuous solution is investigated. The full asymptotic expansions are constructed, when the solution of a nonperturbed problem contains two shock waves.
Biography
Graduate from Bashkir State University (BSU) in 1998. (department of differential equations).
Main publications:
Rasskazov I. O. Vozmuschenie udarnoi volny // TMF, t. 118, # 3, 1999, s. 462–466.
Rasskazov I. O. Slabye vozmuscheniya udarnykh voln // Trudy mezhd. konf. "Kompl. analiz, diff. uravneniya i smezhnye voprosy." II. Differentsialnye uravneniya. Chast I. s. 129–134, 2000, IM s VTs UNTs RAN.
Rasskazov I. O. Vozmuschenie obobschennykh resheniya uravneniya Khopfa // Sbornik trudov regionalnoi shk.-konferentsii dlya stud. asp. i mol. uchenykh po matematike i fizike, t. 1, Izd. BashGU, Ufa 2001, s. 179.
I. O. Rasskazov, “Asymptotics of solutions of a perturbed problem on decay of a discontinuity”, Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003), 143–158; Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S168–S183
2002
2.
I. O. Rasskazov, “The Riemann problem for the weakly perturbed $2\times2$ hyperbolic systems”, Zap. Nauchn. Sem. POMI, 285 (2002), 194–206; J. Math. Sci. (N. Y.), 122:5 (2004), 3564–3571
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