Self-similar blow-up in parabolic equations of Monge--Amp\`ere type
C.R. Budd, V.A. Galaktionov
TL;DR
This paper introduces nonlinear parabolic Monge--Ampère type equations that exhibit various blow-up behaviors, including regional, single point, and global blow-up, along with a related fourth-order flow model.
Contribution
It presents new Monge--Ampère type equations with self-similar blow-up solutions and extends the analysis to a fourth-order flow model.
Findings
Existence of regional, single point, and global blow-up solutions.
Derivation of a related fourth-order Monge--Ampère flow.
Identification of self-similar blow-up patterns.
Abstract
We propose nonlinear parabolic equations of Monge--Amp\'ere (M--A) type that admit regional, single poin, and global blow-up of similarity type. A similar model is derived for a fourth-order M--A flow.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations