We develop in this paper the first systematic treatment of th e homogeneous Boltzmann equation for granular gases with non constant res ti ution coefficient, generalizing a large number of theâ€¦ (More)

The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the spaceâ€¦ (More)

In this paper, we study basic properties of the diffusive wave approximation of the shallow water equations (DSW). This equation is a doubly non-linear diffusion equation arising in shallow waterâ€¦ (More)

We study integrability properties of a general version of the Boltzmann collision operator for hard and soft potentials in n-dimensions. A reformulation of the collisional integrals allows us toâ€¦ (More)

We revisit our recent contribution [2] and give two simpler proofs of the socalled Haffâ€™s law for granular gases (with non-necessarily constant restitution coefficient). The first proof is based uponâ€¦ (More)

In this short note we revisit the gain of integrability property of the gain part of the Boltzmann collision operator. This property implies the W l,r k regularity propagation for solutions of theâ€¦ (More)

We revisit and extend the L p theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis. We introduce new ideas based inâ€¦ (More)

We consider the n-dimensional space homogeneous Boltzmann equation for elastic collisions for variable hard potentials with Grad (angular) cutoff. We prove sharp moment inequalities, the propagationâ€¦ (More)

This short note complements the recent paper of the authors [2]. We revisit the results on propagation of regularity and stability using Lp estimates for the gain and loss collision operators whichâ€¦ (More)

This manuscript investigates the following aspects of the one dimensional dissipative Boltzmann equation associated to variable hard-spheres kernel: (1) we show the optimal cooling rate of the modelâ€¦ (More)