On the problem of determining the parameters of a layered elastic medium and an impulse source.
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 profiles of nonlinear geometric optics
On the quenching of solutions of the wave equation with a nonlinear boundary condition.
On the regularity of boundary traces for the wave equation
On the regularity properties of non-linear wave equations
On the relation of delay equations to first-order hyperbolic partial differential equations
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a single first-order hyperbolic partial differential equation under the effect of measurable inputs acting on...
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
On the sign of Colombeau functions and applications to conservation laws
A generalized concept of sign is introduced in the context of Colombeau algebras. It extends the sign of the point-value in the case of sufficiently regular functions. This concept of generalized sign is then used to characterize the entropy condition for discontinuous solutions of scalar conservation laws.
On the singularities of 3-D Protter's problem for the wave equation.
On the solution -dimensional of the product operator and diamond Bessel operator.
On the solution of the nonlinear wave equation by the decomposition method.
On the solution of transonic flows with weak shocks
On the solution sets of some nonconvex hyperbolic differential inclusions
On the solvability of a Darboux type non-characteristic spatial problem for the wave equation.
On the solvability of a multidimensional version of the Goursat problem for a second order hyperbolic equation with characteristic degeneration.
On the solvability of a spatial problem of Darboux type for the wave equation.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the solvability of the multidimensional version of the first Darboux problem for a model second-order degenerating hyperbolic equation.