On the problem of determining the structure of a layered medium and the shape of an impulse source.
On the problem of symmetrization of hyperbolic equations
The aspects of symmetrization of hyperbolic equations which will be considered in this review have their own history and are related to some classical results from other areas of mathematics ([12]). Here symmetrization means representation of an initial system of equations in the form of a symmetric t-hyperbolic system in the sense of Friedrichs. Some equations of mathematical physics, for example, the equations of acoustics, of gas dynamics, etc. already have this form. In the 70's S. K. Godunov...
On the problem of the Marangoni-to-Prandtl boundary layer transition.
On the profiles of nonlinear geometric optics
On the propagation of singularities of semi-convex functions
On the propagation of surface electromagnetic waves analogous to Rayleigh waves in the case of Leontovich boundary conditions.
On the properties of infinity-harmonic functions and an application to capacitary convex rings.
On the properties of linear differential equations of the second order in the complex domain
On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type
In this paper we consider nonconvex evolution inclusions driven by time dependent convex subdifferentials. First we establish the existence of a continuous selection for the solution multifunction and then we use that selection to show that the solution set is path connected. Two examples are also presented.
On the pullback equation
On the qualitative theory of parametrized families of free boundaries.
On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
On the quasiuniqueness of solutions of degenerate equations in Hilbert space.
On the quenching of solutions of the wave equation with a nonlinear boundary condition.
On the question of existence of a solution to the Tricomi problem for one class of systems of mixed-type equations.
On the radial solutions of a degenerate quasilinear elliptic equation in
On the radially symmetric solutions of a BVP for a class of nonlinear elliptic partial differential equations.
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data . The analytic initial data can be extended as holomorphic functions in a strip around the -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
On the range of convolution operators on non-quasianalytic ultradifferentiable functions
Let denote the non-quasianalytic class of Beurling type on an open set Ω in . For the surjectivity of the convolution operator is characterized by various conditions, e.g. in terms of a convexity property of the pair and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator between ultradistributions of Roumieu type whenever . These...