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The flux function may be discontinuous with respect to both the space variable x and the unknown quantity u.
Such considerations lead us to write arrival rate functions that depend on both the space variable X and the jump size x.
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Our approach allows to handle various numerical discretizations both in the space variables and in the time variable.
We assume that the elliptic operators A have leading coefficients which are in the class of vanishing mean oscillations both in the time variable and the space variable.
The nonlinear term may be singular with respect to both the time and the space variables.
Second, a nonlinear term permits singularities with respect to both the time and the space variables.
At the same time, the nonlinearity f in this paper permits singularities with respect to both the time and the space variables which is seldom considered at present.
The nonlinearity f may be singular both on the time and the space variables.
In this way we can deal with f singular in both its space variables.
Spectral collocation method (pseudospectral method) is applied for discretizing both the space and time variables based on the Jacobi Gauss Lobatto (JGL) interpolation points.
We study the homogenization problem for a random parabolic operator with coefficients rapidly oscillating in both the space and time variables and with a large highly oscillating nonlinear potential, in a general stationary and mixing random media, which is periodic in space.
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