Mild solution of the parabolic equation driven by a $\sigma $-finite stochastic measure

2019 ◽  
Vol 97 ◽  
pp. 17-32
Author(s):  
O. O. Vertsimakha ◽  
V. M. Radchenko
Keyword(s):  
Parabolic Equation ◽  
Mild Solution ◽  
Stochastic Measure

scholarly journals On a nonlocal problem for parabolic equation with time dependent coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Duc Phuong ◽  
Ho Duy Binh ◽  
Le Dinh Long ◽  
Dang Van Yen
Keyword(s):  
Parabolic Equation ◽  
Mild Solution ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Nonlocal Problem ◽  
Point Theory ◽  
Time Dependent ◽  
Well Posedness ◽  
Conformable Derivative

AbstractThis paper is devoted to the study of existence and uniqueness of a mild solution for a parabolic equation with conformable derivative. The nonlocal problem for parabolic equations appears in many various applications, such as physics, biology. The first part of this paper is to consider the well-posedness and regularity of the mild solution. The second one is to investigate the existence by using Banach fixed point theory.

scholarly journals Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure

2019 ◽  
pp. 12-17
Author(s):  
I. M. Bodnarchuk
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Mild Solution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Absolute Value ◽  
Stochastic Measure ◽  
The Cauchy Problem ◽  
Three Dimensional Space ◽  
General Stochastic

We study the Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.

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.

Sign in / Sign up

Export Citation Format

Share Document