Attractors for a Random Evolution Equation with Infinite Memory: An Application

2018 ◽  
pp. 215-236
Author(s):  
María J. Garrido-Atienza ◽  
Björn Schmalfuß ◽  
José Valero
Keyword(s):  
Evolution Equation ◽  
Random Evolution ◽  
Infinite Memory

scholarly journals Attractors for a random evolution equation with infinite memory: Theoretical results

2017 ◽  
Vol 22 (5) ◽  
pp. 1779-1800 ◽  
Author(s):  
Tomás Caraballo ◽  
◽  
María J. Garrido-Atienza ◽  
Björn Schmalfuss ◽  
José Valero ◽  
...  
Keyword(s):  
Evolution Equation ◽  
Random Evolution ◽  
Infinite Memory ◽  
Theoretical Results

Large deviations for random evolution equation in Besov-Orlicz space

2020 ◽  
pp. 357-387
Author(s):  
Dina Miora Rakotonirina ◽  
Jocelyn Hajaniaina Andriatahina ◽  
Rado Abraham Randrianomenjanahary ◽  
Toussaint Joseph Rabeherimanana
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Orlicz Space ◽  
Evolution Equations ◽  
Random Evolution ◽  
Young Function ◽  
Large Deviations Principle

In this paper, we develop a large deviations principle for random evolution equations to the Besov-Orlicz space $\mathcal{B}_{M_2, w}^{v, 0}$ corresponding to the Young function $M_2(x)=\exp(x^2)-1$.

scholarly journals Stroock-Varadhan support theorem for random evolution equation in Besov-Orlicz spaces

2020 ◽  
pp. 187-203
Author(s):  
Jocelyn Hajaniaina Andriatahina ◽  
Dina Miora Rakotonirina ◽  
Toussaint Joseph Rabeherimanana
Keyword(s):  
Differential Equation ◽  
Evolution Equation ◽  
Stochastic Differential Equation ◽  
Stochastic Processes ◽  
Orlicz Space ◽  
Modulus Of Continuity ◽  
Orlicz Spaces ◽  
Random Evolution ◽  
Support Theorem ◽  
The Family

We consider the family of stochastic processes $X=\{X_t, t\in [0;1]\}\,,$ where $X$ is the solution of the It\^{o} stochastic differential equation \[dX_t = \sigma(X_t, Z_t)dW_t + b(X_t,Y_t) dt \hspace*{2cm}\] whose coefficients Lipschitzian depend on $Z=\{Z_t, t\in [0;1]\} $ and $Y=\{Y_t, t\in [0;1]\}$. We prove that the trajectories of $X$ a.s. belong to the Besov-Orlicz space defined by the f nction $M(x)=e^{x^2}-1$ and the modulus of continuity $\omega(t)=\sqrt{t\log(1/t)}$. The aim of this work is to characterize the support of the law $X$ in this space.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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