Related papers: Reconstruction of the collision kernel in the nonl…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
In this short note, we investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data. The main technique is based on higher order linearization and monotonicity approaches. With these methods at…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving…
We investigate the Boltzmann equation with spatial smearing, diffusive boundary conditions, and Lions' collision kernel. Both, the physical as well as the velocity space, are assumed to be bounded. Existence and uniqueness of a stationary…
In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lam\'e parameters with certain regularity assumptions. In…
This paper presents a general framework for constructing reduced models that approximate the Boltzmann equation with arbitrary orders of accuracy in terms of the Knudsen number $\mathit{Kn}$, applicable to general collision models in…
In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the…
In this work we prove global stability for the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse power intermolecular potentials, $r^{-(p-1)}$ with $p>2$. This completes…
In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish several simultaneous recovery results…
In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection…
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
This article is devoted to the study of existence of a mass conserving global solution for the collision-induced nonlinear fragmentation model which arises in particulate processes, with the singular type of collision kernel. The above…
Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
A non-linear Boltzmann equation describing the time evolution of a partonic system in the central rapidity region after a heavy ion collision is solved numerically. A particular model of the collinear logarithmic divergences due to small…
We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…