Linear parabolic problems with dynamic boundary conditions in spaces of Hölder continuous functions

2014 ◽  
Vol 195 (1) ◽  
pp. 167-198 ◽  
Author(s):  
Davide Guidetti
Keyword(s):  
Boundary Conditions ◽  
Continuous Functions ◽  
Parabolic Problems ◽  
Dynamic Boundary Conditions ◽  
Hölder Continuous ◽  
Dynamic Boundary ◽  
Hölder Continuous Functions

scholarly journals Higher-order exponential integrators for constrained semi-linear parabolic problems

2020 ◽  
Vol 2 (1) ◽  
pp. 14-20
Author(s):  
Johannes Wiedemann
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Dynamic ◽  
Order Of Convergence ◽  
Parabolic Systems ◽  
Higher Order ◽  
Parabolic Problems ◽  
Dynamic Boundary Conditions ◽  
Exponential Integrators ◽  
Dynamic Boundary

This paper provides an introduction to exponential integrators for constrained parabolic systems. In addition, building on existing results, schemes with an expected order of convergence of three and four are established and numerically tested on parabolic problems with nonlinear dynamic boundary conditions. The simulations reinforce the subjected error behaviour.

scholarly journals Continuous solutions to two iterative functional equations

2021 ◽  
Author(s):  
Karol Baron
Keyword(s):  
Probability Measure ◽  
Functional Equations ◽  
Continuous Functions ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hölder Continuous Functions

AbstractBased on iteration of random-valued functions we study the problem of solvability in the class of continuous and Hölder continuous functions $$\varphi $$ φ of the equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ \varphi (x)=F(x)+\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ), \end{aligned}$$ φ ( x ) = F ( x ) - ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , φ ( x ) = F ( x ) + ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , where P is a probability measure on a $$\sigma $$ σ -algebra of subsets of $$\Omega $$ Ω .

Sign in / Sign up

Export Citation Format

Share Document