Results 51 to 60 of about 225 (63)
Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species. [PDF]
J Math Biol, 2022 Giunta V, Hillen T, Lewis MA, Potts JR.
europepmc +1 more source
Advanced Nonlinear StudiesIn this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia +2 more
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Semiclassical scattering amplitude at the maximum point of the potential [PDF]
arXiv, 2007 We compute the scattering amplitude for Schr\"odinger operators at a critical energy level, corresponding to the maximum point of the potential. We follow the wrok of Robert and Tamura, '89, using Isozaki and Kitada's representation formula for the scattering amplitude, together with results from Bony, Fujiie, Ramond and Zerzeri '06 in order to analyze
arxiv
Resolvent and scattering matrix at the maximum of the potential [PDF]
arXiv, 2007 We study the microlocal structure of the resolvent of the semi-classical Schrodinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semi-classical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed ...
arxiv
Critical points of solutions of degenerate elliptic equations in the plane [PDF]
arXiv, 2008 We study the minimizer u of a convex functional in the plane which is not G\^ateaux-differentiable. Namely, we show that the set of critical points of any C^1-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler-Lagrange equation that u must satisfy.
arxiv
Level set methods for finding saddle points of general Morse index [PDF]
arXiv, 2010 For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach is motivated by the multidimensional mountain pass theorem, and extends our earlier work on methods (based on ...
arxiv
The location of the hot spot in a grounded convex conductor [PDF]
arXiv, 2010 We investigate the location of the (unique) hot spot in a convex heat conductor with unitary initial temperature and with boundary grounded at zero temperature. We present two methods to locate the hot spot: the former is based on ideas related to the Alexandrov-Bakelmann-Pucci maximum principle and Monge-Amp\`ere equations; the latter relies on ...
arxiv
Existence and symmetry results for competing variational systems [PDF]
arXiv, 2012 In this paper we consider a class of gradient systems of type $$ -c_i \Delta u_i + V_i(x)u_i=P_{u_i}(u),\quad u_1,..., u_k>0 \text{in}\Omega, \qquad u_1=...=u_k=0 \text{on} \partial \Omega, $$ in a bounded domain $\Omega\subseteq \R^N$. Under suitable assumptions on $V_i$ and $P$, we prove the existence of ground-state solutions for this problem ...
arxiv
$L_p$-theory for a Cahn-Hilliard-Gurtin system [PDF]
arXiv, 2012 In this paper we study a generalized Cahn-Hilliard equation which was proposed by Gurtin. We prove the existence and uniqueness of a local-in-time solution for a quasilinear version, that is, if the coefficients depend on the solution and its gradient. Moreover we show that local solutions to the corresponding semilinear problem exist globally as long ...
arxiv
Some principles for mountain pass algorithms, and the parallel distance [PDF]
arXiv, 2012 The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We point out that a good global mountain pass algorithm should have good local and global properties.
arxiv