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On partial differential equations modified with fractional operators and integral transformations: Nonlocal and nonlinear PDF models
(2018-05-04)
We explore nonlocal and pseudo-differential operators in the setting of partial differential equations (PDE). The two primary PDE in this work are the generalized heat equation and the nonlocal Burgers' type advection-diffusion ...
Reduced order framework for optimal control of nonlinear partial differential equations: ROM-based optimal flow control
(2018-05-02)
A variety of partial differential equations (PDE) can govern the spatial and time evolution of fluid flows; however, direct numerical simulation (DNS) of the Euler or Navier-Stokes equation or other traditional computational ...