Asymptotic Properties of the Solutions to Stochastic KPP Equations
TLDR
In this article, a reduction method is used to prove the existence and uniqueness of strong solutions to stochastic Kolmogorov-Petrovskii-Piskunov (KPP) equations, where the initial condition may be anticipating.Abstract:
A reduction method is used to prove the existence and uniqueness of strong solutions to stochastic Kolmogorov–Petrovskii–Piskunov (KPP) equations, where the initial condition may be anticipating. The asymptotic behaviour of the solution for large time and space and the random travelling waves are then studied under two different basic assumptions.read more
Citations
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Optimal Control of Stochastic Partial Differential Equations
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A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.’s
TL;DR: In this paper, a probabilistic representation for a wide class of linear deterministic p.d. equations with potential terms is established, including the wave equation in spatial dimensions 1 to 3.
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Two Properties of Stochastic KPP Equations: Ergodicity and Pathwise Property
TL;DR: In this article, the authors studied the random approximate traveling wave solutions of the stochastic KPP equations and showed that the lower limit of 1 t t 0 u(s, x) ds as t →∞ is positive, and ahead of the wavefront, the limit is zero.
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Travelling Waves in Monostable and Bistable Stochastic Partial Differential Equations
TL;DR: In this paper, the authors provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion (RBD) stochastically partial differential equations (SPDEs).
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A Feynman-Kac-type formula for the deterministic and stochastic wave equations
TL;DR: In this paper, a probabilistic representation for a wide class of linear deterministic p.d.s with potential term was established, including the wave equation in spatial dimensions 1 to 3.
References
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Book
Stability and Complexity in Model Ecosystems
Robert M. May,N. MacDonald +1 more
TL;DR: Preface vii Preface to the Second Edition Biology Edition 1.
Book
Shock Waves and Reaction-Diffusion Equations
TL;DR: In this paper, the basics of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley, are presented in a way accessible to a wider audience than just mathematicians.
Reference BookDOI
Stochastic partial differential equations
TL;DR: Preliminaries Linear and Semilinear Wave Equations of the Second Order Asymptotic Behavior of Solutions Introduction Ito's Formula and Lyapunov Functionals Boundedness of Solutions Stability of Null Solution Invariant Measures Small Random Perturbation Problems Large deviation Problems Large deviations Problems as mentioned in this paper.