A note on Fisher information hypocoercive decay for the linear Boltzmann equation

On the exponential decay to equilibrium of the degenerate linear Boltzmann equation

The dissipative linear Boltzmann equation

We introduce and discuss a linear Boltzmann equation describing dissipative interactions of a gas of test particles with a fixed background. For a pseudo-Maxwellian collision kernel, it is shown that, if the initial distribution has finite temperature, the solution converges exponentially for large–time to a Maxwellian profile drifting at the same velocity as field particles and with a universa...

Quantum linear Boltzmann equation

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the cl...

Note On: Exact Solitary Waves of the Fisher Equation

Kudryashov in [ Phys. Lett. A 342 (2005) 99-106] used simplest nonlinear differential equations like the Riccati equation, the equation for the Jacobi elliptic function to present a new approach for searching exact solutions of nonlinear partial differential equations. As application, he obtained a kind of exact solutions to the Fisher equation. In this letter, more explicit exact solitary wave...

Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation

We consider an inhomogeneous linear Boltzmann equation, with an external confining potential. The collision operator is a simple relaxation toward a local Maxwellian, therefore without diffusion. We prove the exponential time decay toward the global Maxwellian, with an explicit rate of decay. The methods are based on hypoelliptic methods transposed here to get spectral information. They were in...