Results 1 to 10 of about 1,101,646 (327)
Entire solutions for the heat equation
Electronic Journal of Differential Equations, 2021 We consider the solutions of the heat equation $$ \partial_t F = \partial_z^2 F $$ which are entire in z and t (caloric functions). We examine the relation of the z-order and z-type of an entire caloric function \(F(t, z)\), viewed as function of z, to its t-order and t-type respectively, if it is viewed as function of \(t\). Also, regarding the zeros \
Vassilis G. Papanicolaou +2 more
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Adaptive regularization using the entire solution surface. [PDF]
Biometrika, 2009 Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L1- and L∞-norms, that adapts to a variety of situations including sparseness and nonsparseness ...
Wu S, Shen X, Geyer CJ.
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Entire solutions of the euler—poisson equations [PDF]
Ukrainian Mathematical Journal, 2004 ???????????????? ?????? ???????? ????????'???????? ?????????????? ???????????? -????????????????.
A. V. Belyaev
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Entire solutions of diffusive Lotka-Volterra system [PDF]
Journal of Differential Equations, 2020 This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system \begin{equation}\label{eq:abstract} \begin{cases} u_{t}= u_{xx} + u(1-u-av), & \qquad \ x\in\mathbb{R} \cr v_{t}= d v_{xx}+ rv(1-v-bu), & \qquad \ x\in\mathbb{R} \end{cases} \quad (1) \end{equation} where $d,r,a$, and $b$ are ...
King-Yeung Lam +2 more
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Entire solutions of Donaldson’s equation [PDF]
Pacific Journal of Mathematics, 2012 A serious blunder was found in a previous version of the ...
Weiyong He
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Negatively Invariant Sets and Entire Solutions [PDF]
Journal of Dynamics and Differential Equations, 2010 Negatively invariant compact sets of autonomous and nonautonomous dynamical systems on a metric space, the latter formulated in terms of processes, are shown to contain a strictly invariant set and hence entire solutions. For completeness the positively invariant case is also considered. Both discrete and continuous time systems are considered.
Kloeden, Peter E., Marín Rubio, Pedro
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Entire Solutions of Hydrodynamical Equations with Exponential Dissipation [PDF]
Communications in Mathematical Physics, 2009 29 pages, 3 figures, Comm. Math.
Uriel Frisch +5 more
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Nonradial entire solutions for Liouville systems
Journal of Differential Equations, 2017 18 pages, accepted on Journal of Differential ...
Battaglia, Luca +2 more
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Entire solutions to the Monge–Ampère equation
Journal of Mathematical Analysis and Applications, 2010 AbstractWe consider the Monge–Ampère equation det(D2u)=Ψ(x,u,Du) in Rn, n⩾3, where Ψ is a positive function in C2(Rn×R×Rn). We prove the existence of convex solutions, provided there exist a subsolution of the form u̲=a|x|2 and a superharmonic bounded positive function φ satisfying: Ψ>(2a+Δφn)n.
Saoussen Kallel-Jallouli +1 more
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Entire solutions of nonlinear differential-difference equations [PDF]
SpringerPlus, 2016 In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result ...
Cuiping Li, Junfeng Xu, Feng Lü
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