Solving of second order nonlinear PDE problems by using artificial controls with controlled error

다국어 초록 (Multilingual Abstract)

In this paper, we nd the approximate solution of a secondorder nonlinear partial dierential equation on a simple connected regionin R2. We transfer this problem to a new problem of second order non-linear partial dierential equation on a rectangle. Then, we transformedthe later one to an equivalent optimization problem. Then we considerthe optimization problem as a distributed parameter system with articialcontrols. Finally, by using the theory of measure, we obtain the approxi-mate solution of the original problem. In this paper also the global errorin L1 is controlled.

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