Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity
Michael Salins
Abstract
A condition is identified that implies that solutions to the stochastic reaction-diffusion equation ∂u ∂t=Au+f(u)+σ(u)W˙ on a bounded spatial domain never explode. We consider the case where σ grows polynomially and f is polynomially dissipative, meaning that f strongly forces solutions toward finite values. This result demonstrates the role that the deterministic forcing term f plays in preventing explosion.
Topics & Concepts
MathematicsDissipative systemBounded functionMultiplicative noiseMultiplicative functionReaction–diffusion systemDomain (mathematical analysis)Forcing (mathematics)DiffusionTerm (time)Mathematical analysisApplied mathematicsPhysicsAnalog signalQuantum mechanicsElectrical engineeringDigital signal processingSignal transfer functionThermodynamicsEngineeringAdvanced Mathematical Modeling in EngineeringStochastic processes and financial applicationsMathematical Biology Tumor Growth