scholarly journals Existence and uniqueness of mild solution to fractional stochastic heat equation

2018 ◽  
pp. 57-79 ◽  
Author(s):  
Kostiantyn Ralchenko ◽  
Georgiy Shevchenko
Keyword(s):  
Heat Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Stochastic Heat Equation

scholarly journals Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain

2021 ◽  
Author(s):  
Michael Salins
Keyword(s):  
Heat Equation ◽  
Existence And Uniqueness ◽  
Global Solutions ◽  
Spatial Domain ◽  
Stochastic Heat Equation ◽  
The Stochastic Heat Equation ◽  
Dynamic Weighting ◽  
Osgood Condition

We prove the existence and uniqueness of global solutions to the semilinear stochastic heat equation on an unbounded spatial domain with forcing terms that grow superlinearly and satisfy an Osgood condition [Formula: see text] along with additional restrictions. For example, consider the forcing [Formula: see text]. A new dynamic weighting procedure is introduced to control the solutions, which are unbounded in space.

scholarly journals Fractional stochastic heat equation with piecewise constant coefficients

2020 ◽  
Vol 21 (01) ◽  
pp. 2150002
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko ◽  
Mounir Zili ◽  
Eya Zougar
Keyword(s):  
Diffusion Coefficient ◽  
Heat Equation ◽  
Divergence Form ◽  
Stochastic Heat Equation ◽  
Piecewise Constant ◽  
Constant Diffusion Coefficient ◽  
Infinite Dimensional ◽  
Order Elliptic Operator ◽  
Constant Diffusion ◽  
Constant Coefficients

We introduce a fractional stochastic heat equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

Sign in / Sign up

Export Citation Format

Share Document