Impacts of Gaussian noises on the blow-up times of nonlinear stochastic partial differential equations

DOI10.1016/j.nonrwa.2011.10.011zbMath1239.60065OpenAlexW2037965961MaRDI QIDQ425981

Bin Xie, Min Niu

Publication date: 10 June 2012

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.10.011

zbMATH Keywords

Brownian motionimpactgamma distributionblow-up timenonlinear stochastic partial differential equation

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (9)

Estimates of blow‐up times of a system of semilinear SPDEs ⋮ The probability of events for stochastic parabolic equations ⋮ On a generalized population dynamics equation with environmental noise ⋮ Well-posedness of mild solutions to stochastic parabolic partial functional differential equations ⋮ Blow-up solutions of the stochastic nonlocal heat equations ⋮ Blowup of parabolic equations with additive noise ⋮ Impacts of noise on a class of partial differential equations ⋮ Global and non-global solutions of a fractional reaction-diffusion equation perturbed by a fractional noise ⋮ Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain

Cites Work

• Unnamed Item
• On almost periodic mild solutions for stochastic functional differential equations
• Random fuzzy differential equations under generalized Lipschitz condition
• On a Burgers type nonlinear equation perturbed by a pure jump Lévy noise in \(\mathbb R^d\)
• Effect of noise on front propagation in reaction-diffusion equations of KPP type
• The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion
• Blow-up and stability of semilinear PDEs with gamma generators
• Small random perturbations of a dynamical system with blow-up
• A mathematical-model approach to human population explosions caused by migration
• A minicourse on stochastic partial differential equations. Papers based on the presentations at the minicourse, Salt Lake City, UT, USA, May 8--19, 2006.
• Exponential functionals of Brownian motion. I: Probability laws at fixed time
• Finite-time blowup and existence of global positive solutions of a semi-linear SPDE
• Nonlinear stochastic wave equations: blow-up of second moments in \(L^{2}\)-norm
• White noise driven SPDEs with reflection
• The critical parameter for the heat equation with a noise term to blow up in finite time.
• A local-time correspondence for stochastic partial differential equations
• The moment and almost surely exponential stability of stochastic heat equations
• Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations
• Exponential functionals of Brownian motion and related processes

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