On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces I.
On coupling of a first order hyperbolic system with an elliptic equation.
On Jeffreys model of heat conduction
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
On representation of a solution to a modified Cauchy problem.
On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems.
On some boundary value problems for one mixed equation with discontinuous coefficients in a rectangular domain.
On steady compressible Navier-Stokes equations in plane domains with corners.
On the linear force-free fields in bounded and unbounded three-dimensional domains
Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.
On the mixed partial differential equations in n independent variables
On the parabolic potentials in degenerate-type heat equation.
On the question of existence of a solution to the Tricomi problem for one class of systems of mixed-type equations.
On the regularity of the variational solution of the Tricomi problem in the elliptic region
On the solution of transonic flows with weak shocks
On the solvability of boundary value problems for a quasilinear system of equations of mixed and composite type in a multidimensional domain.
On two boundary value problems for mixed type equations with perpendicular lines of type change.
On Uniqueness of Frankl-Morawetz Problem in ...2.
On weak solutions of semilinear hyperbolic-parabolic equations.
One-dimensional model describing the non-linear viscoelastic response of materials
In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Paramétrix et propagation des singularités pour un problème de Cauchy à multiplicité variable
Perturbation index of linear partial differential-algebraic equations with a hyperbolic part
This paper deals with linear partial differential-algebraic equations (PDAEs) which have a hyperbolic part. If the spatial differential operator satisfies a Gårding-type inequality in a suitable function space setting, a perturbation index can be defined. Theoretical and practical examples are considered.