Self-similarity for Ballistic Aggregation Equation
نویسندگان
چکیده
We consider ballistic aggregation equation for gases in which each particle is identified either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as convergence to the self-similarity for generic solutions. For some classes of mass and/or impulsion dependent rates we are also able to estimate the large time decay of some moments of generic solutions or to build some new classes of self-similar solutions.
منابع مشابه
Existence of self-similar profile for a kinetic annihilation model
We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability α ∈ (0, 1) or they undergo an elastic collision with probability 1− α. For such a model, the number of particles, the linear momentum and...
متن کاملSelf-Similar Blowup Solutions to an Aggregation Equation in Rn
We present numerical simulations of radially symmetric finite time blowup for the aggregation equation ut = ∇ · (u∇K ∗ u), where the kernel K(x) = |x|. The dynamics of the blowup exhibits self-similar behavior in which zero mass concentrates at the core at the blowup time. Computations are performed in Rn for n between 2 and 10 using a method based on characteristics. In all cases studied, the ...
متن کاملSelf-similar Blowup Solutions to an Aggregation Equation in R
We present numerical simulations of radially symmetric finite time blowup for the aggregation equation ut = ∇ · (u∇K ∗ u), where the kernel K(x) = |x|. The dynamics of the blowup exhibits self-similar behavior in which zero mass concentrates at the core at the blowup time. Computations are performed in R for n between 2 and 10 using a method based on characteristics. In all cases studied, the s...
متن کاملUniqueness of the self-similar profile for a kinetic annihilation model
We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability α ∈ (0, 1) or they undergo an elastic collision with probability 1 − α. The existence of a self-similar profile for α smaller...
متن کاملFront propagation and critical gradient transport models
This paper analyzes the properties of a two-field critical gradient model that couples a heat equation to an evolution equation for the turbulence intensity. It is shown that the dynamics of a perturbation is ballistic or diffusive depending on the shape of the pulse and also on the distance of the temperature gradient to the instability threshold. This dual character appears in the linear resp...
متن کامل