Related papers: A Diffusion Problem with Neumann Boundary Control …
The Graetz problem is a convection-diffusion equation in a pipe invariant along a direction. The contribution of the present work is to propose a mathematical analysis of the Neumann, Robin and periodic boundary condition on the boundary of…
In this paper, we aim to explore optimal regional trajectory tracking control problems of the anomalous subdiffusion processes governed by time-fractional diffusion systems under the Neumann boundary conditions. Using eigenvalue theory of…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the…
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller…
We study the limit, when $k\to\infty$, of the solutions $u=u_{k}$ of (E) $\prt_{t}u-\Delta u+ h(t)u^q=0$ in $\BBR^N\ti (0,\infty)$, $u_{k}(.,0)=k\delta_{0}$, with $q>1$, $h(t)>0$. If $h(t)=e^{-\gw(t)/t}$ where $\gw>0$ satisfies to…
For any $-1<m<0$, $\mu>0$, $0\le u_0\in L^{\infty}(R)$ such that $u_0(x)\le (\mu_0 |m||x|)^{\frac{1}{m}}$ for any $|x|\ge R_0$ and some constants $R_0>1$ and $0<\mu_0\leq \mu$, and $f,\,g \in C([0,\infty))$ such that $f(t),\, g(t) \geq…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
One proves that the moving interface of a two-phase Stefan problem on $\ooo\subset\rr^d$, $d=1,2,3,$ is controllable at the end time $T$ by a Neumann boundary controller $u$. The phase-transition region is a mushy region $\{\sigma^u_t;\…
A system manager dynamically controls a diffusion process Z that lives in a finite interval [0,b]. Control takes the form of a negative drift rate \theta that is chosen from a fixed set A of available values. The controlled process evolves…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
Let $\Omega$ be a smooth bounded domain in $\R^n$, $n\ge 3$, $0<m\le\frac{n-2}{n}$, $a_1,a_2,..., a_{i_0}\in\Omega$, $\delta_0=\min_{1\le i\le i_0}{dist }(a_i,\1\Omega)$ and let…
Our aim is to study the limit of the solution of reaction-diffusion porous medium equation with linear drift $\displaystyle\partial_t u -\Delta u^m +\nabla \cdot (u \: V)=g(t,x,u) $, as $m\to\infty.$ We study the problem in bounded domain…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
In this work, we consider a nonlocal Fisher-KPP reaction-diffusion problem with Neumann boundary condition and nonnegative initial data in a bounded domain in $\mathbb{R}^n (n \ge 1)$, with reaction term $u^\alpha(1-m(t))$, where $m(t)$ is…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to…