Singular Limit Problem for Some Elliptic Systems

2007 ◽  
Vol 38 (6) ◽  
pp. 1886-1911 ◽  
Author(s):  
Yoshihito Oshita
Keyword(s):  
Elliptic Systems ◽  
Limit Problem ◽  
Singular Limit

Existence of semiclassical ground-state solutions for semilinear elliptic systems

2012 ◽  
Vol 142 (4) ◽  
pp. 867-895 ◽  
Author(s):  
Jun Wang ◽  
Junxiang Xu ◽  
Fubao Zhang
Keyword(s):  
Ground State ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Ground State Solution ◽  
Limit Problem ◽  
State Solution ◽  
Ground State Solutions ◽  
Semilinear Elliptic ◽  
Small Positive Parameter ◽  
Image Position

This paper is concerned with the following semilinear elliptic equations of the formwhere ε is a small positive parameter, and where f and g denote superlinear and subcritical nonlinearity. Suppose that b(x) has at least one maximum. We prove that the system has a ground-state solution (ψε, φε) for all sufficiently small ε > 0. Moreover, we show that (ψε, φε) converges to the ground-state solution of the associated limit problem and concentrates to a maxima point of b(x) in certain sense, as ε → 0. Furthermore, we obtain sufficient conditions for nonexistence of ground-state solutions.

Scale analysis of a hydrodynamic model of plasma

2014 ◽  
Vol 25 (02) ◽  
pp. 371-394 ◽  
Author(s):  
Donatella Donatelli ◽  
Eduard Feireisl ◽  
Antonín Novotný
Keyword(s):  
Hydrodynamic Model ◽  
Debye Length ◽  
Careful Analysis ◽  
Euler System ◽  
Limit Problem ◽  
Singular Limit ◽  
Scale Analysis ◽  
Small Ratio ◽  
High Reynolds ◽  
Incompressible Euler

We examine a hydrodynamic model of the motion of ions in plasma in the regime of small Debye length, a small ratio of the ion/electron temperature, and high Reynolds number. We analyze the associated singular limit and identify the limit problem — the incompressible Euler system. The result leans on careful analysis of the oscillatory component of the solutions by means of Fourier analysis.

scholarly journals A singular limit problem for the Ibragimov-Shabat equation

2016 ◽  
Vol 9 (3) ◽  
pp. 661-673 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Limit Problem ◽  
Singular Limit
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