On the selfsimilar solutions of a diffusion convection equation
The question on finding of radial solutions to a certain degenerate elliptic equation on \(\mathbb{R}^N\), \(N\geq 1\), is reduced to the question on the existence of solutions to the boundary value problem \[ (|u'|^{p-2}u')'+\frac{N-1}{r}|u'|^{p-2}u'+\varepsilon|u'|^q+\beta ru'+\alpha u=0, \;r>0, \quad u(0)=\mu,\;u'(0)=0, \] where \(p>2\), \(q\geq 1\), \(\varepsilon=\pm 1\), and \(\alpha\), \(\beta\) and \(\mu\) are fixed parameters. An existence and uniqueness theorem for the above-mentioned problem is proved. The existence and asymptotic behaviour of positive solutions to the considered problem is studied.
scientific article; zbMATH DE number 1837010