Time-periodic solutions to quasilinear hyperbolic systems with time-periodic boundary conditions

2020 ◽  
Vol 139 ◽  
pp. 356-382
Author(s):  
Peng Qu
Keyword(s):  
Boundary Conditions ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Hyperbolic Systems ◽  
Periodic Boundary Conditions ◽  
Quasilinear Hyperbolic Systems ◽  
Time Periodic Solutions ◽  
Time Periodic

Time-periodic solutions to a nonlinear wave equation with periodic or anti-periodic boundary conditions

2008 ◽  
Vol 465 (2103) ◽  
pp. 895-913 ◽  
Author(s):  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Main Concept ◽  
Time Periodic Solutions ◽  
Time Periodic

This paper is concerned with the existence of time-periodic solutions to the nonlinear wave equation with x -dependent coefficients u ( x ) y tt − ( u ( x ) y x ) x + au ( x ) y +| y | p −2 y = f ( x ,  t ) on (0,  π )× under the periodic or anti-periodic boundary conditions y (0, t )=± y ( π ,  t ), y x (0,  t )=± y x ( π ,  t ) and the time-periodic conditions y ( x ,  t + T )= y ( x ,  t ), y t ( x ,  t + T )= y t ( x ,  t ). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. A main concept is the notion ‘weak solution’ to be given in §2. For T =2 π / k ( k ∈ ), we establish the existence of time-periodic solutions in the weak sense by investigating some important properties of the wave operator with x -dependent coefficients.

Time-periodic solutions to the one-dimensional wave equation with periodic or anti-periodic boundary conditions

2007 ◽  
Vol 137 (2) ◽  
pp. 349-371 ◽  
Author(s):  
Shuguan Ji ◽  
Yong Li
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Boundary Conditions ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Dimensional Wave

This paper is devoted to the study of time-periodic solutions to the nonlinear one-dimensional wave equation with x-dependent coefficients u(x)ytt – (u(x)yx)x + g(x,t,y) = f(x,t) on (0,π) × ℝ under the periodic boundary conditions y(0,t) = y(π,t), yx(0,t) = yx(π,t) or anti-periodic boundary conditions y(0, t) = –y(π,t), yx[0,t) = – yx(π,t). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. Our main concept is that of the ‘weak solution’. For T, the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.

scholarly journals PERIODIC SOLUTIONS OF THE VLASOV–POISSON SYSTEM WITH BOUNDARY CONDITIONS

2000 ◽  
Vol 10 (05) ◽  
pp. 651-672 ◽  
Author(s):  
M. BOSTAN ◽  
F. POUPAUD
Keyword(s):  
Boundary Conditions ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Space Dimension ◽  
Periodic Boundary Conditions ◽  
Small Data ◽  
Poisson System ◽  
One Dimensional ◽  
The One ◽  
Time Periodic

We study the Vlasov–Poisson system with time periodic boundary conditions. For small data we prove existence of weak periodic solutions in any space dimension. In the one-dimensional case the result is stronger: we obtain existence of mild solution and uniqueness of this solution when the data are smooth. It is necessary to impose a nonvanishing condition for the incoming velocities in order to control the lifetime of particles in the domain.

Time-periodic solutions of symmetric hyperbolic systems

2020 ◽  
Vol 17 (04) ◽  
pp. 707-726
Author(s):  
Masashi Ohnawa ◽  
Masahiro Suzuki
Keyword(s):  
Periodic Solutions ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Unique Existence ◽  
Periodic Problems ◽  
Time Periodic Solutions ◽  
External Forces ◽  
Initial Boundary Value ◽  
Time Periodic

We prove the unique existence of time-periodic solutions to general hyperbolic equations with periodic external forces autonomous or nonautonomous over a domain bounded by two parallel planes, provided that all the characteristics with respect to the direction normal to the planes have the same sign. It is also shown that global-in-time solutions to initial-boundary value problems coincide with the solutions to corresponding time-periodic problems after a finite time. We devote one section to the reformulation of several realistic problems and see our results have wide applicability.

scholarly journals Numerical simulation of natural convection in an inclined porous cavity under time-periodic boundary conditions with a partially active thermal side wall

RSC Advances ◽  
2017 ◽  
Vol 7 (28) ◽  
pp. 17519-17530 ◽  
Author(s):  
Feng Wu ◽  
Gang Wang
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Side Wall ◽  
Periodic Boundary Conditions ◽  
Porous Cavity ◽  
Thermal Boundary Conditions ◽  
The Right ◽  
Time Periodic

Natural convection in an inclined porous cavity with positively or negatively inclined angles is studied numerically for time-periodic boundary conditions on the left side wall and partially active thermal boundary conditions on the right wall.

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