Results 41 to 50 of about 671 (73)
Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems [PDF]
Journal of Nonlinear Mathematical Physics, Vol. 21, No. 4
(December 2014), 643--671, 2014 We present a complete description of $2$-dimensional equations that arise as symmetry reductions of fourf $3$-dimensional Lax-integrable equations: (1) the universal hierarchy equation~$u_{yy}=u_zu_{xy}-u_yu_{xz}$; (2) the 3D rdDym equation $u_{ty}=u_xu_{xy}-u_yu_{xx}$; (3) The basic Veronese web equation $u_{ty}=u_tu_{xy}-u_yu_{tx}$; (4) Pavlov's ...
arxiv +1 more source
Monotonicity and symmetry of singular solutions to quasilinear problems
, 2018 We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved moving plane ...
Esposito, Francesco +2 more
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Advanced Nonlinear StudiesIn this paper, we consider the general dual fractional parabolic problem ∂tαu(x,t)+Lu(x,t)=f(t,u(x,t))inRn×R. ${\partial }_{t}^{\alpha }u\left(x,t\right)+\mathcal{L}u\left(x,t\right)=f\left(t,u\left(x,t\right)\right) \text{in} {\mathbb{R}}^{n}{\times ...
Guo Yahong, Ma Lingwei, Zhang Zhenqiu
doaj +1 more source
Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation
, 2019 The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $-\Delta u = u-u^3-\delta$ in $\R^N$, with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder.
Rizzi, Matteo
core +1 more source
Multiple solutions to a magnetic nonlinear Choquard equation
, 2011 We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\ $is a real valued vector potential, $V$ is a real valued scalar ...
A. Ambrosetti +27 more
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The properties of a new fractional g-Laplacian Monge-Ampère operator and its applications
Advances in Nonlinear AnalysisIn this article, we first introduce a new fractional gg-Laplacian Monge-Ampère operator: Fgsv(x)≔infP.V.∫Rngv(z)−v(x)∣C−1(z−x)∣sdz∣C−1(z−x)∣n+s∣C∈C,{F}_{g}^{s}v\left(x):= \inf \left\{\hspace{0.1em}\text{P.V.}\hspace{0.1em}\mathop{\int }\limits_{{{\mathbb{
Wang Guotao, Yang Rui, Zhang Lihong
doaj +1 more source
, 2013 We consider the semilinear Lane Emden problem in a smooth bounded simply connected domain in the plane, invariant by the action of a finite symmetry group G.
De Marchis, Francesca +2 more
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Harmonic approximation and improvement of flatness in a singular perturbation problem [PDF]
arXiv, 2014 We study the De Giorgi type conjecture, that is, one dimensional symmetry problem for entire solutions of an two components elliptic system in $\mathbb{R}^n$, for all $n\geq 2$. We prove that, if a solution $(u,v)$ has a linear growth at infinity, then it is one dimensional, that is, depending only on one variable. The main ingredient is an improvement
arxiv
Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics
European Journal of Applied MathematicsContemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements.
Maryam Ahmadpoortorkamani +1 more
doaj +1 more source
A new proof of Savin's theorem on Allen-Cahn equations [PDF]
arXiv, 2014 In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on the uniform $C^{1,\alpha}$ regularity of flat level sets, which then implies the one dimensional symmetry of minimizers in $\mathbb{R}^n$ for $n\leq 7$.
arxiv