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Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE’s with a Small Parameter
Quasi linear parabolic equations parameters quasi linear initial boundary value
2015/9/28
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
Metastability for Non-Linear Random Perturbations of Dynamical Systems
Quasi linear parabolic equation the small parameter the second order items
2015/9/28
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding di@...
First-order SODE: OU processdX+aX(t)dt= dW(t)
Three options:a >0, a= 0, a <0.
First-order SPDE:du= au
xx dt+dW(t, x)
One option:a >0(Infinite-dimensional stable OU process.)
Second-order SODE:X¨ ...
Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems
nonlinear dynamical systems nonlinear equations parameterized models
2011/1/17
We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter s...