A Periodic Problem

2021 ◽  
Vol 385 (5) ◽  
pp. e17
Author(s):  
Allison Kratka ◽  
Nicholas Yozamp ◽  
Anand Vaidya ◽  
Ellen Marqusee
Keyword(s):  
Periodic Problem

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

Periodic problem for nonlinear Ablowitz model

1993 ◽  
Vol 65 (6) ◽  
pp. 1921-1927
Author(s):  
Yu. N. Sidorenko ◽  
A. K. Prikarpatskii
Keyword(s):  
Periodic Problem

Periodic problem for the classical two-dimensional Thirring model

1980 ◽  
Vol 31 (4) ◽  
pp. 362-367
Author(s):  
A. K. Prikarpatskii ◽  
P. I. Golod
Keyword(s):  
Periodic Problem ◽  
Thirring Model ◽  
Two Dimensional

scholarly journals Pairs of nodal solutions for a Minkowski-curvature boundary value problem in a ball

2019 ◽  
Vol 21 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Alberto Boscaggin ◽  
Maurizio Garrione
Keyword(s):  
Boundary Value Problem ◽  
Neumann Problem ◽  
Boundary Value ◽  
Periodic Problem ◽  
Nodal Solutions ◽  
Shooting Technique ◽  
One Dimensional ◽  
Dimensional Equation

By using a shooting technique, we prove that the quasilinear boundary value problem [Formula: see text] where [Formula: see text] is a ball and [Formula: see text], has more and more pairs of nodal solutions on growing of the parameter [Formula: see text]. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.

The inverse doubly periodic problem of fracture mechanics for a composite reinforced with unidirectional fibres

2019 ◽  
Vol 24 (10) ◽  
pp. 3254-3278 ◽  
Author(s):  
Vagif Mirsalimov
Keyword(s):  
Optimal Design ◽  
Periodic System ◽  
Periodic Problem ◽  
Theoretical Work ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Elastic Fibres ◽  
Load Bearing Capacity ◽  
Composite Body ◽  
Doubly Periodic Problem

A theoretical analysis is made of the optimal interference for fitting elastic fibres into the two-periodic system of holes of an isotropic elastic binder. The principles of equal strength and the minimization of stress intensity factors are used. The binder of the composite is weakened by a doubly periodic system of rectilinear cracks. A criterion and methods for solving the problem of the prevention of fracture of a composite reinforced with unidirectional fibres are suggested. A closed system of algebraic equations that allows one to obtain the solution of the problem of the optimal design of a composite body depending on the mechanical and geometrical characteristics of a binder and fibre is constructed. The found interference provides an increase of the load-bearing capacity of the composite. The results of the considered theoretical work open new possibilities for the optimal design of the composite bodies (composites) at the expense of the choice of interference of the binder and fibre joint.

scholarly journals Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions

2000 ◽  
Vol 43 (3) ◽  
pp. 569-586 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Nikolaos Yannakakis
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Operator ◽  
Periodic Problem ◽  
Distributed Parameter ◽  
Pseudomonotone Operators ◽  
Evolution Inclusions ◽  
Evolution Triple ◽  
Relaxation Theorem ◽  
Strong Relaxation ◽  
Surjectivity Result

AbstractWe study the existence of extremal periodic solutions for nonlinear evolution inclusions defined on an evolution triple of spaces and with the nonlinear operator establish A being time-dependent and pseudomonotone. Using techniques of multivalued analysis and a surjectivity result for L-generalized pseudomonotone operators, we prove the existence of extremal periodic solutions. Subsequently, by assuming that A(t, ·) is monotone, we prove a strong relaxation theorem for the periodic problem. Two examples of nonlinear distributed parameter systems illustrate the applicability of our results.

scholarly journals Periodic Problem with a Potential Landesman Lazer Condition

2010 ◽  
Vol 2010 (1) ◽  
pp. 586971 ◽  
Author(s):  
Petr Tomiczek
Keyword(s):  
Periodic Problem
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