On a reliable solution of a quasilinear elliptic equation with uncertain coefficients: sensitivity analysis and numerical examples

On the worst scenario method: A modified convergence theorem and its application to an uncertain differential equation

“…Quasilinear elliptic boundary value problems with uncertain coefficients were studied in [2], [3], [6], [7], see also [4,Chapter III]. In these works the coefficient of the state equation is a u-dependent function.…”

On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

“…Quasilinear elliptic boundary value problems with uncertain coefficients were studied in [6], [7], [1], [2], see also [9,Chapter III]. This paper, primarily, generalizes the one-dimensional problem examined in [5] to a two-dimensional uncertain partial differential equation.…”

Worst scenario method in homogenization. Linear case

“…On the rest of the boundary, the Dirichlet condition u 0 = 0 is given. This model problem was inspired by the example shown in [6]. Let us recall that the functional Φ is in the form Φ(u 0 (A 0 (A, χ(A)))) = 1 |Ω| Ω u 0 (A 0 (A, χ(A)))) dx.…”