IN the six lectures before us, Prof. Prasad gives an interesting account of the part played by partial differential equations in dealing with vibratory phenomena, conduction of heat, gravitational ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

Physics-informed neural networks (PINNs) represent a burgeoning paradigm in computational science, whereby deep learning frameworks are augmented with explicit physical laws to solve both forward and ...

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

This work establishes the first asymptotic stability result for multi-wave patterns in damped wave equations with partially linearly degenerate flux. The authors prove that global solutions converge ...

This is the 2nd part of a two course graduate sequence in analytical methods to solve partial differential equations of mathematical physics. Review of Separation of variables. Laplace Equation: ...