Boundary solutions

1982 ◽  
Vol 14 (2) ◽  
pp. 117
Author(s):  
Computational Mechanics Centre
Keyword(s):  
Boundary Solutions

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

scholarly journals Blow up boundary solutions of some semilinear fractional equations in the unit ball

2016 ◽  
Vol 140 ◽  
pp. 236-253 ◽  
Author(s):  
Mohamed Ben Chrouda ◽  
Mahmoud Ben Fredj
Keyword(s):  
Unit Ball ◽  
Blow Up ◽  
Fractional Equations ◽  
Boundary Solutions

Free boundary solutions to a log-singular elliptic equation

2013 ◽  
Vol 82 (1-2) ◽  
pp. 91-107 ◽  
Author(s):  
Marcelo Montenegro ◽  
Sebastián Lorca
Keyword(s):  
Elliptic Equation ◽  
Free Boundary ◽  
Singular Elliptic Equation ◽  
Boundary Solutions

Searching for a Model of Multiple‐Site Recreation Demand that Admits Interior and Boundary Solutions

1995 ◽  
Vol 77 (1) ◽  
pp. 129-140 ◽  
Author(s):  
Edward R. Morey ◽  
Donald Waldman ◽  
Djeto Assane ◽  
Douglass Shaw
Keyword(s):  
Recreation Demand ◽  
Multiple Site ◽  
Boundary Solutions
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