scholarly journals Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tran Ngoc Thach ◽  
Devendra Kumar ◽  
Nguyen Hoang Luc ◽  
Nguyen Huy Tuan
Keyword(s):  
Parabolic Equation ◽  
White Noise ◽  
Linear Space ◽  
Parabolic Equations ◽  
Caputo Derivative ◽  
Direct Problem ◽  
Mild Solutions ◽  
Fractional Caputo Derivative ◽  
Existence And Regularity Results ◽  
Regularity Results

<p style='text-indent:20px;'>Solutions of a direct problem for a stochastic pseudo-parabolic equation with fractional Caputo derivative are investigated, in which the non-linear space-time-noise is assumed to satisfy distinct Lipshitz conditions including globally and locally assumptions. The main aim of this work is to establish some existence, uniqueness, regularity, and continuity results for mild solutions.</p>

scholarly journals Regularity of Wong-Zakai approximation for non-autonomous stochastic quasi-linear parabolic equation on $ {\mathbb{R}}^N $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guifen Liu ◽  
Wenqiang Zhao
Keyword(s):  
Differential Equation ◽  
Parabolic Equation ◽  
White Noise ◽  
Parabolic Equations ◽  
Growth Exponent ◽  
Linear Parabolic Equation ◽  
Approximation Technique ◽  
Linear Parabolic Equations ◽  
Random Attractors ◽  
Multiplicative White Noise

<p style='text-indent:20px;'>In this paper, we investigate a non-autonomous stochastic quasi-linear parabolic equation driven by multiplicative white noise by a Wong-Zakai approximation technique. The convergence of the solutions of quasi-linear parabolic equations driven by a family of processes with stationary increment to that of stochastic differential equation with white noise is obtained in the topology of <inline-formula><tex-math id="M2">\begin{document}$ L^2( {\mathbb{R}}^N) $\end{document}</tex-math></inline-formula> space. We establish the Wong-Zakai approximations of solutions in <inline-formula><tex-math id="M3">\begin{document}$ L^l( {\mathbb{R}}^N) $\end{document}</tex-math></inline-formula> for arbitrary <inline-formula><tex-math id="M4">\begin{document}$ l\geq q $\end{document}</tex-math></inline-formula> in the sense of upper semi-continuity of their random attractors, where <inline-formula><tex-math id="M5">\begin{document}$ q $\end{document}</tex-math></inline-formula> is the growth exponent of the nonlinearity. The <inline-formula><tex-math id="M6">\begin{document}$ L^l $\end{document}</tex-math></inline-formula>-pre-compactness of attractors is proved by using the truncation estimate in <inline-formula><tex-math id="M7">\begin{document}$ L^q $\end{document}</tex-math></inline-formula> and the higher-order bound of solutions.</p>

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Existence and regularity results for unilateral problems with degenerate coercivity

2019 ◽  
Vol 69 (6) ◽  
pp. 1351-1366 ◽  
Author(s):  
Hocine Ayadi ◽  
Rezak Souilah
Keyword(s):  
Penalty Method ◽  
Degenerate Coercivity ◽  
Unilateral Problems ◽  
Existence And Regularity Results ◽  
Regularity Results

Abstract In this paper we prove some existence and regularity results for nonlinear unilateral problems with degenerate coercivity via the penalty method.

An inverse source problem for pseudo-parabolic equation with Caputo derivative

2021 ◽  
Author(s):  
Le Dinh Long ◽  
Nguyen Hoang Luc ◽  
Salih Tatar ◽  
Dumitru Baleanu ◽  
Nguyen Huu Can
Keyword(s):  
Parabolic Equation ◽  
Caputo Derivative ◽  
Inverse Source Problem
Sign in / Sign up

Export Citation Format

Share Document