English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we derive general theorems for controlling (vector-valued)first order ordinary differential equations such that its solutions stop at afinite time $T>0$ and apply them to relaxation and dissipative oscillationprocesses. We discuss several interesting examples for relaxation processeswith finite stopping time and their energy behaviour. Our results on relaxationand dissipative oscillations enable us to model diffusion processes with finitefront speeds and dissipative waves that cause in each space point $x$ anoscillation with a finite stopping time $T(x)$. In the latter case, we derivethe relation between $T(0)$ and $T(x)$. Moreover, the relations beteween thecontrol functions in the ode model and the respective pde model are derived.Inparticular, we present an application of the Paley-Wiener-Schwartz Theorem thatis used in our analysis. A complementary approach for dissipative oscillationsand its application to dissipative waves is presented in [Ko19b], where thefinite stopping time is achieved due to nonconstant coefficients in secondorder odes.

Dynamical systems with finite stopping times. Part 1: Relaxation, oscillation and their application to diffusion and wave dissipation