Über die Existenz von unendlich vielen periodischen Lösungen einer einfachen Temperaturregelung.
Un théorème de valeurs intermédiaires dans les espaces de Sobolev et applications
Unbeschränkte Randwerte bei parabolischen Differentialgleichungen.
Unconditionally Stable Explicit Methods for Parabolic Equations.
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...
Uniform bounds for solutions of a degenerate diffusion equation with nonlinear boundary conditions
Unique global solvability of 1D Fried-Gurtin model
We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified assumptions...
Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.
In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equationb(u)t - div (|∇u - k(b(u))e|p-2 (∇u - k(b(u))e)) + g(x,u) = f(t,x).This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines, etc. The solvability of this problem is established in the BVt(Q) space....
Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.
Uniqueness of bounded solutions to a viscous diffusion equation.
Uniqueness of solutions to a class of strongly degenerate parabolic equation.
Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics.