In this paper, we explain in simple PDE terms a famous result of Bramson about the loga-
rithmic delay of the position of the solutions u (t, x) of Fisher-KPP reaction-diffusion …

In this review, we provide a concise summary of several important mathematical results for
stochastic travelling waves generated by monostable and bistable reaction-diffusion …

In this paper we study the effect of the addition of a convective term, and of the resulting
increased dissipation rate, on the growth of solutions to a general class of non-linear …

We consider semilinear parabolic equations of the form\begin {equation*} u_t= u_ {xx}+ f
(u),\quad x\in\mathbb {R}, t> 0,\end {equation*} where $ f $ a $ C^ 1$ function. Assuming that …

In this paper we investigate a variety of deep learning strategies for solving inverse
problems. We classify existing deep learning solutions for inverse problems into three …

This paper is concerned with an optimal control problem governed by a semilinear,
nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous …

We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson
which asserts that, in the case of a spatially homogeneous reaction rate, the time lag …

We study reaction–diffusion equations in one spatial dimension and with general (space-or
time-) inhomogeneous mixed bistable–ignition reactions. For those satisfying a simple …

We consider a coarse-grained neural field model for synaptic activity in spatially extended
cortical tissue that possesses an underlying periodicity in its microstructure. The model is …

We introduce DeepParticle, a method to learn and generate invariant measures of stochastic
dynamical systems with physical parameters based on data computed from an interacting …