Reconstruction of the Collision Kernel in the Nonlinear Boltzmann Equation
From MaRDI portal
Publication:4964798
DOI10.1137/20M1329366zbMath1459.35400arXiv2003.09549OpenAlexW3129405907MaRDI QIDQ4964798
Ru-Yu Lai, Gunther Uhlmann, Yang Yang
Publication date: 4 March 2021
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.09549
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Cites Work
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- An inverse radiative transfer in refractive media equipped with a magnetic field
- Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model
- Formation and propagation of discontinuity for Boltzmann equation in non-convex domains
- Decay and continuity of the Boltzmann equation in bounded domains
- On the Cauchy problem for Boltzmann equations: Global existence and weak stability
- Gauge equivalence in stationary radiative transport through media with varying index of refraction
- The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials
- The Boltzmann equation: global existence for a rare gas in an infinite vacuum
- An inverse boundary value problem for the stationary transport equation
- On the spatially homogeneous Boltzmann equation
- On uniqueness in inverse problems for semilinear parabolic equations
- The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
- Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations
- Inverse problems for semilinear wave equations on Lorentzian manifolds
- Generalized stability estimates in inverse transport theory
- Propagation of boundary-induced discontinuity in stationary radiative transfer and its application to the optical tomography
- An inverse problem for the transport equation in the presence of a Riemannian metric
- On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
- On a quasilinear inverse boundary value problem
- Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
- Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media
- An inverse problem for a semi-linear elliptic equation in Riemannian geometries
- Inverse problems for elliptic equations with power type nonlinearities
- Stability estimates in stationary inverse transport
- Reconstruction for the coefficients of a quasilinear elliptic partial differential equation
- The boundary rigidity problem in the presence of a magnetic field
- Optical tomography in two dimensions
- Inverse Transport with Isotropic Time-harmonic Sources
- Stability of the Gauge equivalent classes in inverse stationary transport in refractive media
- Stability for Time-Dependent Inverse Transport
- Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map
- Inverse problems in quasilinear anisotropic media
- Reconstruction of the coefficients of the stationary transport equation from boundary measurements
- Inverse scattering and inverse boundary value problems for the linear boltzmann equation
- Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit
- Inverse Problems for the Stationary Transport Equation in the Diffusion Scaling
- A remark on partial data inverse problems for semilinear elliptic equations
- Stability of the gauge equivalent classes in inverse stationary transport
- Global Lipschitz stability in determining coefficients of the radiative transport equation