scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

scholarly journals Nonlinear parabolic problems in unbounded domains

1979 ◽  
Vol 82 (3-4) ◽  
pp. 201-209 ◽  
Author(s):  
Guy Mahler
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Unbounded Domains ◽  
Parabolic Problems ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic Problems ◽  
Existence Of Weak Solutions ◽  
Nonlinear Parabolic

We show the existence of weak solutions of nonlinear parabolic partial differential equations in unbounded domains, provided that a variant of the Leray-Lions conditions is satisfied.

STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE

1991 ◽  
Vol 01 (01) ◽  
pp. 41-59 ◽  
Author(s):  
Z. BRZEŹNIAK ◽  
M. CAPIŃSKI ◽  
F. FLANDOLI
Keyword(s):  
Partial Differential Equations ◽  
Global Existence ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Burgers Equations ◽  
Global Existence Of Solutions ◽  
High Regularity

Stochastic partial differential equations are proposed in order to model some turbulence phenomena. A particular case (the stochastic Burgers equations) is studied. Global existence of solutions is proved. Their regularity is also studied in detail. It is shown that the solutions cannot possess too high regularity.

Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations

1994 ◽  
Vol 46 (2) ◽  
pp. 415-437 ◽  
Author(s):  
Tokuzo Shiga
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Stochastic Partial Differential Equation ◽  
Partial Differential ◽  
One Dimensional ◽  
Noise Term

AbstractThe paper is concerned with the comparison of two solutions for a one-dimensional stochastic partial differential equation. Noting that support compactness of solutions propagates with passage of time, we define the SCP property and show that the SCP property and the strong positivity are two contrasting properties of solutions for one-dimensional SPDEs, which are due to degeneracy of the noise-term coefficient

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