8 citations · 13 across the 23 of their papers we have counts for
24 papers
On flows generated by square-integrable vector fields
Nikolay A. Gusev, Mikhail V. Korobkov, Evgeny Yu. Panov +1
For square-integrable divergence-free vector field on we prove that the following properties are equivalent: 1) the operator $A_0 ρ= \boldsymbol{v}…
On symmetric systems of transport equations
Evgeny Yu. Panov
We study a symmetric system of transport equations with solenoidal coefficients. This system reduces to an evolutionary equation with a skew-symmetric spatial operator in the real…
On linear evolutionary equations with skew symmetric spatial operators
Evgeny Yu. Panov
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive sem…
On evolutionary equations related to skew-symmetric spatial operators
Evgeny Yu. Panov
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive…
On self-similar solutions of a multi-phase Stefan problem
Evgeny Yu. Panov
We study self-similar solutions of a multi-phase Stefan problem, first in the case of one space variable, and then in the radial multidimensional case. In both these cases we prove…
On solutions of an ill-posed Stefan problem
Evgeny Yu. Panov
We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational for…
On the structure of entropy solutions to the Riemann problem for a degenerate nonlinear parabolic equation
Evgeny Yu. Panov
We find an explicit form of entropy solutions to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is…
On the structure of weak solutions to the Riemann problem for degenerate nonlinear diffusion equation
Evgeny Yu. Panov
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated tha…
On entropy solutions of scalar conservation laws with discontinuous flux
Evgeny Yu. Panov
We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove existence of the largest and the smallest e.s. to…
On decay of entropy solutions to degenerate nonlinear parabolic equations with perturbed periodic initial data
Evgeny Yu. Panov
Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of period…
On decay of entropy solutions to multidimensional conservation laws in the case of perturbed periodic initial data
Evgeny Yu. Panov
Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux and with initi…
On some properties of entropy solutions of degenerate non-linear anisotropic parabolic equations
Evgeny Yu. Panov
We prove existence of the largest and the smallest entropy solutions to the Cauchy problem for a nonlinear degenerate anisotropic parabolic equation. Applying this result, we estab…
To the theory of entropy sub-solutions of degenerate non-linear parabolic equations
Evgeny Yu. Panov
We prove existence of the largest entropy sub-solution and the smallest entropy super-solution to the Cauchy problem for a nonlinear degenerate parabolic equation with only continu…
On decay of entropy solutions to multidimensional conservation laws
Evgeny Yu. Panov
Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.
Decay of periodic entropy solutions to degenerate nonlinear parabolic equations
Evgeniy Yu. Panov
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
On long time behavior of periodic entropy solutions of a degenerate non-linear parabolic equation
Evgeny Yu. Panov
We prove the asymptotic convergence of a space-periodic entropy solution of a one-dimensional degenerate parabolic equation to a traveling wave. It is also shown that on a segment…
On decay of almost periodic viscosity solutions to Hamilton-Jacobi equations
Evgeny Yu. Panov
We establish that a viscosity solution to a multidimensional Hamilton-Jacobi equation with a convex non-degenerate hamiltonian and Bohr almost periodic initial data decays to its i…
On almost periodic viscosity solutions to Hamilton-Jacobi equations
Evgeny Yu. Panov
We establish that a viscosity solution to a multidimensional Hamilton-Jacobi equation with Bohr almost periodic initial data remains to be spatially almost periodic and the additiv…
On the long time behavior of almost periodic entropy solutions to scalar conservation laws
Evgeny Yu. Panov
We found the precise condition for the decay as of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of…
On one criterion of the uniqueness of generalized solutions for linear transport equations with discontinuous coefficients
Evgeny Yu. Panov
We study generalized solutions of multidimensional transport equation with bounded measurable solenoidal field of coefficients . It is shown that any generalized solution sat…
On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws
Evgeny Yu. Panov
We propose a new sufficient non-degeneracy condition for the strong precompactness of bounded sequences satisfying the nonlinear first-order differential constraints. This result i…
On the Cauchy problem for scalar conservation laws on the Bohr compactification of
Evgeny Yu. Panov
We study the Cauchy problem for a multidimensional scalar conservation law on the Bohr compactification of . The existence and uniqueness of entropy solutions are established…
On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: global well-posedness and decay property
Evgeny Yu. Panov
We study the Cauchy problem for a multidimensional scalar conservation law with merely continuous flux vector in the class of Besicovitch almost periodic functions. The existence a…
On variants of -measures and compensated compactness
Evgeny Yu. Panov
We introduce new variant of -measures defined on spectra of general algebra of test symbols and derive the localization properties of such -measures. Applications for the com…