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February 9, 2026Journal of Mathematical Physics0 citations

Multidimensional stochastic nonlinear pseudoparabolic equations on a hyperoctant with boundary noise

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INIlia NaumkinNSNorma Sotelo-Garcia

Key Points

  • The aim is to establish the existence and uniqueness of solutions to stochastic nonlinear pseudoparabolic equations.
  • Considered stochastic nonlinear pseudoparabolic equations under Dirichlet noise boundary conditions.
  • Analyzed the initial-boundary value problem for local existence and uniqueness.
  • Performed investigations on solution regularity, particularly near the origin.
  • Local existence and uniqueness of solutions were established in appropriate Sobolev spaces.
  • The regularity behavior of solutions was detailed, especially in areas of high irregularity near the boundary.

Abstract

We consider the stochastic nonlinear pseudoparabolic equations on the hyperoctant with Dirichlet noise boundary conditions. We establish the local existence and uniqueness of the solution to the initial-boundary value problem with values in an appropriate Sobolev space. We are also interested in the regularity behavior of the solution, especially near the origin, where the boundary data are highly irregular.

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Cite This Study

Naumkin et al. (2025) studied this question.

synapsesocial.com/papers/698979e9f0ec2af6756e7f32https://doi.org/10.1063/5.0235272
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