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texto impreso
We consider the semilinear parabolic system (S) { ut-?u=vp ; vt-?v=uq, where x ? R(N) (N ? 1), t > 0, and p, q are positive real numbers. At t=0, nonnegative, continuous, and bounded initial values (u0(x), v0(x)) are prescribed. The correspon[...]texto impreso
In this paper we describe the fundamental solution of the equation that is obtained linearizing the Uehling-Uhlenbeck equation around the steady state of Kolmogorov type f(k) = k?7/6. Detailed estimates on its asymptotics are obtained.texto impreso
We study in this paper the asymptotic behaviour of solutions of a nonlinear Fokker-Plank equation. Such an equation describes the evolution of radiation for a gas of photons, which interacts with electrons by means of Compton scattering and Brem[...]texto impreso
Consider the system (S) {ut–?u=v(p),inQ={(t,x),t> 0, x??}, vt–?v=u(q), inQ, u(0,x)=u0(x)v(0,x)=v0(x)in?, u(t,x)=v(t,x)=0, whent?0, x???, where ? is a bounded open domain in ?N with smooth boundary, p and q are positive parameters, and functions[...]texto impreso
Let (u(t, x), v(t, x)) and (uBAR(t, x), vBAR(t, x)) be two nonnegative classical solutions of (S)[GRAPHICS:{ut=?u+vp, p> 0 ; vt=?v+uq, q> 0] in some strip S(T) = (0, T) x R(N), where 0
