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Conductive-radiative heat transfer in a scattering and absorbing medium bounded by two reflecting and radiating plane surfaces is examined. P 1 approximation (diffusion model) is used for the simplification of the original problem. The existence and uniqueness of solutions of the diffusion model are proved. The convergence of an iterative procedure of… (More)

The paper studies the interaction of a periodic solid bristle structure with a fluid. Such problems arise, for example, when modelling biotechnological devices operating in liquids or when simulating epithelium surfaces of blood vessels. The fluid is described by the linearized Navier– Stokes equation whereas the solid part is governed by equations of… (More)

Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution… (More)

A one-dimensional model is derived in order to study how the elasticity (internal elastic energy) of visco-elastic and elasto-plastic materials, such as biopolymers (muscles and grain our dough) or metals, changes due to the action of external forces. For such materials, the model takes the form of an initial-boundary value problem, corresponding to… (More)

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