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We consider a stochastic PDE driven by a parabolic second order partial differential operator with non-constant coefficients and with a nonlinear random external forcing given by a Gaussian noise that is white in time and spatially homogeneous. We prove th ...
Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving differential equations by integrating physical laws into the learning process. This work leverages PINNs to simulate gravitational collapse, a critical phenomenon in astro ...
This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...