scholarly journals Linearly degenerate hierarchies of quasiclassical SDYM type

2017 ◽  
Vol 58 (9) ◽  
pp. 093505 ◽  
Author(s):  
L. V. Bogdanov ◽  
M. V. Pavlov
Keyword(s):  
Linearly Degenerate

A treatment of discontinuities for nonlinear systems with linearly degenerate fields

2007 ◽  
Vol 36 (5) ◽  
pp. 987-1003 ◽  
Author(s):  
Enrique D. Fernández-Nieto ◽  
Vicente Martínez
Keyword(s):  
Nonlinear Systems ◽  
Linearly Degenerate

Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws

2018 ◽  
Vol 24 (2) ◽  
pp. 793-810
Author(s):  
Tatsien Li ◽  
Lei Yu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Front Tracking ◽  
Entropy Solutions ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Quasilinear Hyperbolic Systems ◽  
Exact Boundary ◽  
Systems Of Conservation Laws ◽  
Linearly Degenerate

In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures et Appl. 107 (2017) 1–40; L. Yu, Chinese Ann. Math., Ser. B (To appear)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both ε-approximate front tracking solutions and limit solutions.

Hyperplane-Approximation-Based Method for Many-Objective Optimization Problems with Redundant Objectives

2019 ◽  
Vol 27 (2) ◽  
pp. 313-344
Author(s):  
Yifan Li ◽  
Hai-Lin Liu ◽  
E. D. Goodman
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Approximation Error ◽  
Main Idea ◽  
Benchmark Problems ◽  
Performance Metric ◽  
Dominance Structure ◽  
Objective Reduction ◽  
Pareto Fronts ◽  
Linearly Degenerate

For a many-objective optimization problem with redundant objectives, we propose two novel objective reduction algorithms for linearly and, nonlinearly degenerate Pareto fronts. They are called LHA and NLHA respectively. The main idea of the proposed algorithms is to use a hyperplane with non-negative sparse coefficients to roughly approximate the structure of the PF. This approach is quite different from the previous objective reduction algorithms that are based on correlation or dominance structure. Especially in NLHA, in order to reduce the approximation error, we transform a nonlinearly degenerate Pareto front into a nearly linearly degenerate Pareto front via a power transformation. In addition, an objective reduction framework integrating a magnitude adjustment mechanism and a performance metric [Formula: see text] are also proposed here. Finally, to demonstrate the performance of the proposed algorithms, comparative experiments are done with two correlation-based algorithms, LPCA and NLMVUPCA, and with two dominance-structure-based algorithms, PCSEA and greedy [Formula: see text]MOSS, on three benchmark problems: DTLZ5(I,M), MAOP(I,M), and WFG3(I,M). Experimental results show that the proposed algorithms are more effective.

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