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An example of a nonlinear second order elliptic system in three dimension

Josef DaněčekMarek Nikodým — 2004

Commentationes Mathematicae Universitatis Carolinae

We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two C 0 , γ -regularity theories. We show that, for certain range of parameters, the theory developed in (2002), gives a stronger result than the theory introduced in , 1995. In addition, there is a range of parameters where the first theory gives H"older continuity of solution for all γ < 1 , while the theory is not applicable at all.

Numerical solution of the Kiessl model

Josef DalíkJosef DaněčekJiří Vala — 2000

Applications of Mathematics

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical...

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