Self similar solutions of generalized Burgers equation

Abstract

<p>In this paper, we study the initial-value problem</p> <pre>(|u'|^p-2u')' + βru' + αu - γ|u|^q-1 u|u'|^p-2u' = 0, r > 0,<br> u(0) = A, u'(0) = 0,</pre> <p>where A > 0, p > 2, q > 1, α > 0, β > 0 and γ ∈ ℝ. Existence and complete classification of solutions are established. Asymptotic behavior for nonnegative solutions is also presented.</p>