Blowup for the heat equation with a noise term

DOI10.1007/BF01195068zbMath0792.60056MaRDI QIDQ1326266

Carl E. Mueller, Richard B. Sowers

Publication date: 18 May 1994

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

Dirichlet boundary conditionsbranching processrandom heat equationblowup in finite time

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (23)

The critical parameter for the heat equation with a noise term to blow up in finite time. ⋮ Existence and blow-up of solutions to the fractional stochastic heat equations ⋮ The probability of events for stochastic parabolic equations ⋮ Global solutions to the stochastic reaction-diffusion equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain ⋮ A phase transition for a stochastic PDE related to the contact process ⋮ Blow-up for stochastic reaction-diffusion equations with jumps ⋮ The scaling limit for a stochastic PDE and the separation of phases ⋮ Global existence and finite time blow-up for a stochastic non-local reaction-diffusion equation ⋮ $L^p$ solutions for stochastic evolution equation with nonlinear potential ⋮ Singular initial conditions for the heat equation with a noise term ⋮ Pathwise mild solutions for quasilinear stochastic partial differential equations ⋮ Some non-existence results for a class of stochastic partial differential equations ⋮ Finite time blowup in \(L^2\) sense of solutions to SPDEs with Bernstein functions of the Laplacian ⋮ Explosive solutions of stochastic reaction-diffusion equations in mean \(L^p\)-norm ⋮ Positivity and explosion in mean \(L^p\)-norm of stochastic functional parabolic equations of retarded type ⋮ Blowup solutions for stochastic parabolic equations ⋮ Uniqueness and blow-up for a stochastic viscous dyadic model ⋮ Impacts of noise on a class of partial differential equations ⋮ Time-space white noise eliminates global solutions in reaction-diffusion equations ⋮ Finite-time singularity of the stochastic harmonic map flow ⋮ Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity ⋮ Blow-up results for space-time fractional stochastic partial differential equations ⋮ On non-existence of global solutions to a class of stochastic heat equations

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• Long time existence for the heat equation with a noise term
• Large deviations for a reaction-diffusion equation with non-Gaussian perturbations
• Large deviations for the invariant measure of a reaction-diffusion equation with non-Gaussian perturbations
• Limit results for two stochastic partial differential equations
• On the support of solutions to the heat equation with noise
• Global Existence, Large Time Behavior and Life Span of Solutions of a Semilinear Parabolic Cauchy Problem
• Refined asymptotics for the blowup of u_t — δu = u^p
• Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations

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