Results 1 to 10 of about 1,574 (25)
Singular reduction operators in two dimensions [PDF]
J. Phys. A: Math. Theor. 41 (2008) 505201, 24 pp, 2008 The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to first-order ODEs are are exhaustively described.
arxiv +1 more source
Stability of constant steady states of a chemotaxis model [PDF]
arXiv, 2021 The Cauchy problem for the parabolic--elliptic Keller--Segel system in the whole $n$-dimensional space is studied. For this model, every constant $A \in \mathbb{R}$ is a stationary solution. The main goal of this work is to show that $A < 1$ is a stable steady state while $A > 1$ is unstable.
arxiv
Semi-wavefront solutions in models of collective movements with density-dependent diffusivity [PDF]
arXiv, 2017 This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for instance).
arxiv
Recent Developments on the Ricci Flow [PDF]
arXiv, 1998 This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
arxiv
arXiv, 2006 We study the local well-posedness theory for the Schr\"odinger Maps equation. We work in $n+1$ dimensions, for $n \geq 2$, and prove a local well-posedness for small initial data in $H^{\frac{n}{2}+\e}$.
arxiv
Group Classification of Burgers' Equations [PDF]
arXiv, 2008 In this work we carry out a complete group classification of Burgers' equations.
arxiv
Very singular solutions for the thin film equation with absorption [PDF]
arXiv, 2009 Self-similar large time behaviour of weak solutions of the fourth-order parabolic thin film equations with absorption is studued.
arxiv
Deforming a convex hypersurface with low entropy by its Gauss curvature [PDF]
arXiv, 2015 We prove the asymptotic roundness under normalized Gauss curvature flow provided entropy is initially small enough.
arxiv
A geometric interpretation of Hamilton's Harnack inequality for the Ricci flow [PDF]
Mathematical Research Letters, vol. 2 (1995) 701-718, 2002 We give a geometric interpretation of Hamilton's matrix Harnack inequality for the Ricci flow as the curvature of a connection on space-time.
arxiv
A geometric approach to the linear trace Harnack inequality for the Ricci flow [PDF]
Mathematical Research Letters, vol 2 (1996) 549-568, 2002 We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.
arxiv