On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients
Applications of Mathematics (2011)
- Volume: 56, Issue: 5, page 459-480
- ISSN: 0862-7940
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topHarasim, Petr. "On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients." Applications of Mathematics 56.5 (2011): 459-480. <http://eudml.org/doc/197102>.
@article{Harasim2011,
abstract = {We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. Furthermore, it is shown that the Galerkin approximation of the state solution can be calculated by means of the Kachanov method as the limit of a sequence of solutions to linearized problems.},
author = {Harasim, Petr},
journal = {Applications of Mathematics},
keywords = {worst scenario problem; nonlinear differential equation; uncertain input parameters; Galerkin approximation; Kachanov method; worst scenario problem; nonlinear differential equation; Galerkin approximation},
language = {eng},
number = {5},
pages = {459-480},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients},
url = {http://eudml.org/doc/197102},
volume = {56},
year = {2011},
}
TY - JOUR
AU - Harasim, Petr
TI - On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 5
SP - 459
EP - 480
AB - We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. Furthermore, it is shown that the Galerkin approximation of the state solution can be calculated by means of the Kachanov method as the limit of a sequence of solutions to linearized problems.
LA - eng
KW - worst scenario problem; nonlinear differential equation; uncertain input parameters; Galerkin approximation; Kachanov method; worst scenario problem; nonlinear differential equation; Galerkin approximation
UR - http://eudml.org/doc/197102
ER -
References
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