This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

We propose a new nonconforming finite element algorithm to approximate the solution to the
elliptic problem involving the fractional Laplacian. We first derive an integral representation …

We define a new class of Gaussian processes on compact metric graphs such as street or
river networks. The proposed models, the Whittle–Matérn fields, are defined via a fractional …

In this paper we introduce the critical variational setting for parabolic stochastic evolution
equations of quasi-or semi-linear type. Our results improve many of the abstract results in …

We construct a divergence-free velocity field u:[0, T]× T 2→ R 2 satisfying u∈ C∞([0, T]; C α
(T 2))∀ α∈[0, 1) such that the corresponding drift-diffusion equation exhibits anomalous …

Coupled partial differential equations (PDEs) defined on domains with different
dimensionality are usually called mixed-dimensional PDEs. We address mixed-dimensional …

We consider three problems for the Helmholtz equation in interior and exterior domains in
R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for …

It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

The fractional differential equation $ L^\beta u= f $ posed on a compact metric graph is
considered, where $\beta> 0$ and $ L=\kappa^ 2-\nabla (a\nabla) $ is a second-order …