Morawetz problem for generalized Tricomi equation.
Nonlinear symmetric positive systems
Nonlocal boundary value problems for elliptic-parabolic differential and difference equations.
Non-local problems for parabolic-hyperbolic equations with deviation from the characteristics and three type-changing lines.
Numerical analysis of nonlinear elliptic-parabolic equations
This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern’s iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).
Numerical analysis of nonlinear elliptic-parabolic equations
This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).
Oblique derivative problems for generalized Rassias equations of mixed type with several characteristic boundaries.
On a mixed problem for a coupled nonlinear system.
On a nonlocal problem for a confined plasma in a Tokamak
The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms and , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.
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 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 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 two boundary value problems for mixed type equations with perpendicular lines of type change.
On weak solutions of semilinear hyperbolic-parabolic equations.
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.
Régularité de problèmes aux limites de type Hermite et Tricomi