8 papers
Long-time asymptotics of solutions of the heat equation
Sergei V. Zakharov
The long-time asymptotics of solutions of the Cauchy problem for the heat equation are constructed in the case when the initial function at infinity has power asymptotics.
Large-gradient and Lagrange singularities of solutions of a quasilinear parabolic equation
Sergei V. Zakharov
Asymptotic solutions of a quasilinear parabolic equation with a small parameter at the higher derivative are constructed near large-gradient and Lagrange singularities of A-type, w…
Asymptotics of the convolution of the Airy function and a function of the power-like behavior
Sergei V. Zakharov
The asymptotic behavior of the convolution-integral of a special form of the Airy function and a function of the power-like behavior at infinity is obtained. The integral under con…
Formation of compression waves with multiscale asymptotics in the Burgers and KdV models
Sergei V. Zakharov
The Cauchy problem for the Burgers equation with a small dissipation and an initial weak discontinuity and the Cauchy problem with a large initial gradient for a quasilinear parabo…
Two-parameter asymptotics in the Cauchy problem for a parabolic equation
Sergei V. Zakharov
The Cauchy problem for a quasi-linear parabolic equation with a small parameter at a higher derivative is considered. The initial step-like function contains another small paramete…
Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation
Sergei V. Zakharov
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial…