scholarly journals Existence of the fundamental solution of a second order evolution equation

1997 ◽  
Vol 66 ◽  
pp. 15-35 ◽  
Author(s):  
Jan Bochenek
Keyword(s):  
Fundamental Solution ◽  
Evolution Equation ◽  
Second Order

scholarly journals Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

2016 ◽  
Vol 7 (2) ◽  
pp. 130-149 ◽  
Author(s):  
Lidia Saluto ◽  
Maria Stella Mongioví
Keyword(s):  
Evolution Equation ◽  
Dimensional Analysis ◽  
Unit Volume ◽  
Vortex Formation ◽  
Second Order ◽  
Line Density ◽  
Superfluid Turbulence ◽  
Turbulence Flow ◽  
Vortex Diffusion

Abstract We investigate the evolution equation for the average vortex length per unit volume L of superfluid turbulence in inhomogeneous flows. Inhomogeneities in line density L andincounterflowvelocity V may contribute to vortex diffusion, vortex formation and vortex destruction. We explore two different families of contributions: those arising from asecondorder expansionofthe Vinenequationitself, andthose whichare notrelated to the original Vinen equation but must be stated by adding to it second-order terms obtained from dimensional analysis or other physical arguments.

Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in ℝ2

2018 ◽  
Vol 3 (1) ◽  
pp. 14-18 ◽  
Author(s):  
Chun-Chi Lin ◽  
Yang-Kai Lue
Keyword(s):  
Evolution Equation ◽  
Convergent Subsequence ◽  
Second Order ◽  
Plane Curves ◽  
Smooth Solutions ◽  
Fixed Position ◽  
Elastic Curves ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Abstract For any given C2-smooth initial open curves with fixed position and fixed tangent at the boundary points, we obtain the long-time existence of smooth solutions under the second-order evolution of plane curves. Moreover, the asymptotic limit of a convergent subsequence is an inextensible elastica.

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