Related papers: Mean value methods for solving the heat equation b…
We investigate inverse backward-in-time problems for a class of second-order degenerate Mean-Field Game (MFG) systems. More precisely, given the final datum $(u(\cdot, T),m(\cdot, T))$ of a solution to the one-dimensional mean-field game…
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…
Given a connected compact Riemannian manifold $(M,g)$ without boundary, $\dim M\ge 2$, we consider a space--time fractional diffusion equation with an interior source that is supported on an open subset $V$ of the manifold. The…
We present an efficient, effective, and generic approach towards solving inverse problems. The key idea is to leverage the feedback signal provided by the forward process and learn an iterative update model. Specifically, at each iteration,…
In this short paper we provide a new proof of the geometric Forward-Reverse Brascamp-Lieb inequality, using the approach of the heat semigroup, or the heat flow. Furthermore, we characterize all the Forward-Reverse Brascamp-Lieb data such…
In this paper, we consider an inverse problem to determine a semilinear term of a parabolic equation from a single boundary measurement of Neumann type. For this problem, a reconstruction algorithm is established by the spectral…
We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin boundary and total energy integral overdetermination condition. The well-posedness of the problem is…
For an expensive to evaluate computer simulator, even the estimate of the overall surface can be a challenging problem. In this paper, we focus on the estimation of the inverse solution, i.e., to find the set(s) of input combinations of the…
We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of…
We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…
An inverse-free dynamical system is proposed to solve the generalized absolute value equation (GAVE) with a fixed time convergence, where the time of convergence is finite and is uniformly bounded for all initial points. Moreover, an…
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…
We use the nonstandard Fourier transform method, along with an established nonstandard approach to ODE's, to find a solution to the heat equation, on $(0,\infty)\times\mathcal{R}$, with a given boundary condition $g$ at $t=0$. We use this…
We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
We study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator,…
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to…
We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…