Abstract
Self-similar blow-up solutions for the generalized deterministic KPZ equationut=uxx+|ux|qwithq>2are considered. The asymptotic behavior of self-similar solutions is studied.
Highlights
We consider the generalized deterministic KPZ equation ∂u ∂t = ∂2u ∂x2 + ∂u ∂xq for (x, t) ∈ ST := R × (0, T), (1)where q > 2 and T > 0
We refer to the review article [3] for references and a detailed historical account of the KPZ equation
In this paper we investigate the asymptotic behavior of self-similar blow-up solutions of (1) with q > 2 having the form u (x, t) = (T − t)α f (ξ), (2)
Summary
We consider the generalized deterministic KPZ equation For q ≠ 2 it called the generalized deterministic KPZ equation or The existence and uniqueness of a classical solution of the Cauchy problem for (1) with q = 1 and initial function u0 ∈ C03(Rn) were proven in [4]. The existence and uniqueness of a solution to the Cauchy problem with unbounded initial datum are proved in [12].
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