Objective
This research will be devoted to the mathematical theory of such nonlinear problems in mechanics of solids and fluids as plasticity, visco-plasticity, phase transitions and Non-Newtonian fluids.
These problems are related to materials with highly nonlinear constitutive laws which can be mathematically described by systems of nonlinear differential equations of elliptic or parabolic type. The aim of this work is to investigate mathematical formulations of the corresponding boundary and initial-boundary value problems, proving existence of solutions and to investigate regularity of their solutions.
New qualitative properties of solutions obtained on this step could provide a basis for the analysis of numerical approximations which is another purpose of the proposed research .
In the frame of this study it is planned to obtain a priori and a posteriori error estimates for approximate solutions of the above problems.
Topic(s)
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66041 /OG_
Germany