Variational approach for a class of cooperative systems [PDF]
Nonlinear Analysis, Theory, Methods and Applications, 75 (2012)
5620-5638, 2014 The aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non--local equation through classical variational methods. Thanks to those results we are able to obtain the blow--up behaviour of the solutions in the whole domain for certain ...
arxiv +1 more source
Maximal regularity for parabolic partial differential equations on manifolds with cylindrical ends [PDF]
arXiv, 2008 We give a short, simple proof of maximal regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and the concept of R-boundedness for the resolvent.
arxiv
Ricci flow of conformally compact metrics [PDF]
, 2010 In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We adapt recent results of Schn\"urer, Schulze and Simon to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.
arxiv +1 more source
Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrödinger Equations [PDF]
arXiv, 2011 A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.
arxiv
Boundary De Giorgi-Ladyzhenskaya classes and their application to regularity of swirl of Navier-Stokes [PDF]
arXiv, 2012 The embeddings theorem of space-boundary-type DeGiorgi-Ladyzhenskaya parabolic classes into Holder spaces is presented, which is useful for regularity considerations for parabolic boundary value problems. Additionaly, the application of this theory to Navier-Stokes-s swirl is presented.
arxiv
Multiple peak aggregations for the Keller-Segel system [PDF]
, 2012 In this paper we derive matched asymptotic expansions for a solution of the Keller-Segel system in two space dimensions for which the amount of mass aggregation is $8\pi N$, where $N=1,2,3,...$ Previously available asymptotics had been computed only for the case in which N=1.
arxiv +1 more source
Basic Dynamical Systems Control of Aeroengine Flow [PDF]
arXiv, 2000 The notions of basic controllability and basic control are defined using dynamical systems theory of partial differential equations. A quadratic optimal control of the linearized viscous Moore-Greitzer equation is presented and it is confirmed that stall is uncontrollable in this model.
arxiv
The time-dependent maximum principle for systems of parabolic equations subject to an avoidance set [PDF]
arXiv, 2002 In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to an avoidance set.
arxiv
New conditional symmetries and exact solutions of reaction-diffusion systems with power diffusivities [PDF]
J. Phys. A: Math. Theor. 41 (2008) 185208 (14pp), 2008 A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansatze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are obtained. The relation of the solutions obtained with the development of spatially inhomogeneous structures is ...
arxiv
On self-similar collapse of discontinuous data for thin film equations with doubly degenerate mobility [PDF]
arXiv, 2009 It is shown that a Riemann-type problem with discontinuous data of sign-type for the thin film equation, which degenerates at +1 and -1, admits a self-similar solution. Both FBP and the Cauchy problem (oscillatory solutions near interfaces) settings are taken into account.
arxiv