Many important geometric partial differential equations are Euler–Lagrange equations of natural functionals. Amongst the most prominent examples are harmonic and biharmonic maps between Riemannian ...

This is a preview. Log in through your library . Abstract The explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, ...

The importance of similarity transformations and their applications to partial differential equations is discussed. The theory has been presented in a simple manner so that it would be beneficial at ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...