7 problems

Sharp-edge diffusion-field conjecture. These equations might have a broader domain of validity if $D(x,y)$ and $\widetilde{\mathbf{D}}(x,y)$ are augmented by diffusion fields induc…

Dataset-size conjecture. This discrepancy can be reduced by enlarging the size of the training dataset for each representative correlation length.

The equation considered has parameters $c3_1$, $c3_2$, and $c4$; numerical experiments concern the case $c3_1=c3_2$ with $c4=1$, allowing rupture in several subintervals. Nonexiste…

Let $u$ solve the one-dimensional diffusion equation studied in the paper, and let $U$ be a monotone similarity profile. The linearization around $u=U$ is … with eigenvalues…

Let $f$ be the self-similar profile function of the diffusion equation, let $\eta$ denote its similarity variable, let $D$ be the diffusion coefficient, and let $g$ be an auxiliary…

Let $u_T=\mathcal{K}_T u_0$ be the result of diffusing an image $u_0$ to time $T$, and let $\mathcal{K}_T^{-1}$ denote the inverse diffusion operator. For a time step $\delta t$ wi…

Let $\Omega$ be the spatial domain, let $D$ be the diffusion coefficient, let $\bar G(x,y,0)$ denote the photon flux from $x$ to $y$ in the absence of an ultrasound field, and let…