Non-local dispersal and bistability [PDF]
, 2006 The scalar initial value problem [ u_t = ho Du + f(u), ] is a model for dispersal. Here $u$ represents the density at point $x$ of a compact spatial region $Omega in mathbb{R}^n$ and time $t$, and $u(cdot)$ is a function of $t$ with values in some ...
Hutson, V. +3 more
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Finite elements III: first-order and time-dependent PDEs [PDF]
, 2021 This book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters.
Ern, Alexandre, Guermond, Jean-Luc
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Application of Generalized Logistic Function to Travelling Wave Solutions for a Class of Nonlinear Evolution Equations [PDF]
, 2022 The generalized Logistic function that solves a first-order nonlinear ODE with an arbitrary positive power term of the dependent variable is introduced in this paper, by means of which the traveling wave solutions of a class of nonlinear evolution ...
Jinliang Zhang +2 more
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Continuity equations and ODE flows with non-smooth velocity [PDF]
, 2014 In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this framework, we deal with velocity fields that are not smooth, but
Crippa, Gianluca, Ambrosio, Luigi
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Boundary regularity of stochastic PDEs [PDF]
, 2019 The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly—and in a sense, arbitrarily—bad: as shown by Krylov[ SIAM J. Math.
Gerencser, Mate
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BMO Martingales and Positive Solutions of Heat Equations [PDF]
, 2015 International audienceIn this paper, we develop a new approach to establish gradient estimates for positive solutions to the heat equation of elliptic or subelliptic operators on Euclidean spaces or on Riemannian manifolds.
Hu, Ying, Qian, Zhongmin
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Positive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree [PDF]
, 2018 We study the periodic boundary value problem associated with the second order nonlinear equation u'' + ( λa^+(t) - μa^-(t) ) g(u) = 0, where g(u) has superlinear growth at zero and sublinear growth at infinity.
Zanolin, Fabio +2 more
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Networks & Heterogeneous Media, 2010 We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative stationary solution, which implies that an interface that was flat originally cannot get stationary ...
Coville, Jérôme +2 more
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Determining a parabolic system by boundary observation of its non-negative solutions with biological applications [PDF]
, 2023 In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions.
Lo, Catharine W. K., Liu, Hongyu
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Multiple positive solutions of a Sturm-Liouville boundary value problem with conflicting nonlinearities [PDF]
, 2017 We study the second order nonlinear differential equation u''+∑_i α_ia_i(x)g_i(u) − ∑j β_jb_j(x)k_j(u)=0, where α_i,β_j>0, a_i(x), b_j(x) are non-negative Lebesgue integrable functions defined in [0,L], and the nonlinearities g_i(s), k_j(s) are ...
Feltrin, Guglielmo
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