Displaying similar documents to “Algebraic integrability for minimum energy curves”

Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

Ken Shirakawa (2009)

Banach Center Publications

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In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of...

Multiplication formulas for q-Appell polynomials and the multiple q-power sums

Thomas Ernst (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In the first article on q-analogues of two Appell polynomials, the generalized Apostol-Bernoulli  and Apostol-Euler  polynomials, focus was on generalizations, symmetries, and complementary argument theorems. In this second article, we focus on a recent paper by Luo, and one paper on power sums by Wang and Wang. Most of the proofs are made by using generating functions, and the (multiple) q-addition plays a fundamental role. The introduction of the q-rational numbers in formulas with...

Low Mach number limit of a compressible Euler-Korteweg model

Yajie Wang, Jianwei Yang (2023)

Applications of Mathematics

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This article deals with the low Mach number limit of the compressible Euler-Korteweg equations. It is justified rigorously that solutions of the compressible Euler-Korteweg equations converge to those of the incompressible Euler equations as the Mach number tends to zero. Furthermore, the desired convergence rates are also obtained.