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research article

Lp-regularity theory for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity

Han, Beom-Seok
•
Yi, Jaeyun  
October 26, 2023
Journal Of Differential Equations

We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-diffusion equation (SRDE) with colored noise F-center dot:partial derivative(t)u = aijuxixj +biuxi + cu - bu1+beta +xi u1+gamma F-center dot, (t, x) is an element of R+ x Rd; u(0, ) = u0,where a(ij), b(i), c, b and xi are C-2 or L-infinity bounded random coefficients. Here beta > 0 denotes the degree of strong dissipativity and gamma > 0 represents the degree of stochastic force. Under the reinforced Dalang's condition on F-center dot, we show the well-posedness of the SRDE provided gamma < kappa (beta+1) d+2 where kappa > 0 is the constant related to F-center dot. Our result assures that strong dissipativity prevents the solution from blowing up. Moreover, we provide the maximal H & ouml;lder regularity of the solution in time and space. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

  • Details
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Type
research article
DOI
10.1016/j.jde.2023.10.042
Web of Science ID

WOS:001109357600001

Author(s)
Han, Beom-Seok
Yi, Jaeyun  
Date Issued

2023-10-26

Publisher

Academic Press Inc Elsevier Science

Published in
Journal Of Differential Equations
Volume

379

Start page

569

End page

599

Subjects

Physical Sciences

•

Stochastic Partial Differential Equation

•

Stochastic Reaction-Diffusion Equation

•

Strong Dissipativity

•

Super-Linear, Colored Noise

•

Lp Regularity

•

Holder Regularity

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
PROPDE  
FunderGrant Number

National Research Foundation of Korea (NRF) - Korea government (MSIT)

NRF-2021R1C1C2007792

Samsung Science and Technology Foundation

SSTF-BA1401-51

Available on Infoscience
February 20, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/204443
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