Resonances in the Shukhov tower, in the Sobolev equation, and in the tanks of spin-stabilized rockets

2014 ◽  
pp. 155-160
Keyword(s):  
Sobolev Equation ◽  
Shukhov Tower

scholarly journals Bifurcation analysis of the Hardy-Sobolev equation

2021 ◽  
Vol 296 ◽  
pp. 759-798
Author(s):  
Denis Bonheure ◽  
Jean-Baptiste Casteras ◽  
Francesca Gladiali
Keyword(s):  
Bifurcation Analysis ◽  
Sobolev Equation

On the Hardy–Sobolev equation

2017 ◽  
Vol 147 (2) ◽  
pp. 299-336 ◽  
Author(s):  
E. N. Dancer ◽  
F. Gladiali ◽  
M. Grossi
Keyword(s):  
Sobolev Equation ◽  
Radial Solutions ◽  
Image Position

In this paper we study the problemwhere Ω = ℝN or Ω = B1, N ⩾ 3, p > 1 and . Using a suitable map we transform problem (1) into another one without the singularity 1/|x|2. Then we obtain some bifurcation results from the radial solutions corresponding to some explicit values of λ.

scholarly journals A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jinfeng Wang ◽  
Yang Liu ◽  
Hong Li ◽  
Zhichao Fang
Keyword(s):  
Error Estimates ◽  
Existence And Uniqueness ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Element Solution ◽  
Sobolev Equation ◽  
Priori Error Estimates ◽  
Mixed Element ◽  
Convection Dominated ◽  
Element Method

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classicalH(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates inL2-norm for the scalar unknownuand a priori error estimates in(L2)2-norm for its gradientλand its fluxσ. Moreover, we obtain the optimal a priori error estimates inH1-norm for the scalar unknownu. Finally, we obtained some numerical results to illustrate efficiency of the new method.

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