The dominant asymptotic term of solution to the Hamer equation

Article type: Research Article

Authors: Soloviev, A.A.

Affiliations: Department of Mathematics, Chelyabinsk State University, Chelyabinsk 454001, Russia. Tel.: +7 351 799 72 92; E-mail: [email protected]

Abstract: It is shown that the dominant asymptotic term of solution to the problem ut+uux=K*u−u, u|t=0=u0, where K(x)=(1/2)e−|x|, is a function u0(x,t)=2ζ(x,t)(1−∫−∞xζ(s,t) ds)−1 with ζ(x,t)=M0(h)ex2/4t/√4πt, M0(h)=∫−∞∞h(s) ds and h(x)=(1/2)u0(x)exp {−(1/2)∫−∞xu0(s) ds}, and the function u0(x,t) coincides with the principal asymptotic term of solution to the Burgers equation with initial function u0.

Keywords: radiating gas, initial value problem, asymptotic behavior

DOI: 10.3233/ASY-2012-1122

Journal: Asymptotic Analysis, vol. 81, no. 2, pp. 121-134, 2013