On the Existence of Stationary Solutions to the Povzner Equation in a Bounded Domain
نویسنده
چکیده
The existence of stationary solutions to the Povzner equation is established for a class of problems in bounded domains with smooth boundaries. The result holds for general type collision kernels under assumptions of angular cutoo. The boundary conditions with xed in-data and with a linear operator of diiuse reeection type are considered. The method is based on constructing approximate solutions by a strong xed point argument and establishing their weak compactness using estimates for the entropy production.
منابع مشابه
On the Interior Boundary-Value Problem for the Stationary Povzner Equation with Hard and Soft Interactions
The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angula...
متن کاملEXISTENCE OF A STEADY FLOW WITH A BOUNDED VORTEX IN AN UNBOUNDED DOMAIN
We prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. The data prescribed is the rearrangement class of the vorticity field. The corresponding stream function satisfies a semilinear elliptic partial differential equation. The result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...
متن کاملUncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...
متن کاملStationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain
In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in R
متن کاملPolynomially bounded solutions of the Loewner differential equation in several complex variables
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$, where $A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [A(tau)...
متن کامل