The jump problem for mixed-type equations with defects on the type change line.
The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition
We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition with a locally defined, -bounded function . We prove the existence of a local weak solution to the problem by means of the Rothe method. A uniform a priori estimate for the Rothe approximations in , which is required by the local assumptions on , is derived by...
The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions...
The Volterra property of some problems with the Bitsadze–Samarskiĭ-type conditions for a mixed parabolic-hyperbolic equation.
Time-delay regularization of anisotropic diffusion and image processing
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Time-delay regularization of anisotropic diffusion and image processing
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Tykhonov well-posedness of a heat transfer problem with unilateral constraints
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by . We associate to Problem an optimal control problem, denoted by . Then, using appropriate Tykhonov triples, governed by a nonlinear operator and a convex , we provide results concerning the well-posedness of problems...
Über eine spezielle Differentialgleichung vom gemischten Typ im R3.
Über Randwertprobleme für Gleichungen vom gemischten Typ im (II)
Über Randwertprobleme für Gleichungen vom gemischten Typ im (I)
Un problema de transmisión no lineal de tipo hiperbólico-parabólico.
Uniqueness of entropy solutions of nonlinear elliptic-parabolic-hyperbolic problems in one dimension space.
Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems.
Uniqueness of solutions to a class of strongly degenerate parabolic equation.
Uniqueness results for the Minkowski problem extended to hedgehogs
The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.
Young measure solutions for nonlinear evolutionary systems of mixed type
Асимптотика решения смешанной задачи для системы дифференциальных уравнений, связанной с положительным интегральным оператором
Видоизмененная задача трикоми для уравнения
Граничная задача М для одной системы уравнений смешнного типа
Две задачи со смещениями для уравнения смешанно-составного типа