Large time existence of small viscous surface waves without surface tension

1990 ◽  
Vol 15 (6) ◽  
pp. 823-903 ◽  
Author(s):  
Donna Lynn ◽  
Gates Sylvester
Keyword(s):  
Surface Tension ◽  
Surface Waves ◽  
Large Time ◽  
Time Existence

scholarly journals Large Time Existence of Special Strong Solutions to MHD Equations in Cylindrical Domains

2017 ◽  
Vol 20 (3) ◽  
pp. 1013-1034
Author(s):  
Bernard Nowakowski ◽  
Gerhard Ströhmer ◽  
Wojciech M. Zaja̧czkowski
Keyword(s):  
Large Time ◽  
Strong Solutions ◽  
Mhd Equations ◽  
Cylindrical Domains ◽  
Time Existence

Nonlinear Neumann boundary value problem for semilinear heat equations with critical power nonlinearities

2021 ◽  
pp. 1-35
Author(s):  
Nakao Hayashi ◽  
Elena I. Kaikina ◽  
Pavel I. Naumkin ◽  
Takayoshi Ogawa
Keyword(s):  
Boundary Value Problem ◽  
Large Time ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Heat Equations ◽  
Semilinear Heat Equation ◽  
Neumann Boundary Value Problem ◽  
Time Existence ◽  
Time Asymptotic Behavior

We study the nonlinear Neumann boundary value problem for semilinear heat equation ∂ t u − Δ u = λ | u | p , t > 0 , x ∈ R + n , u ( 0 , x ) = ε u 0 ( x ) , x ∈ R + n , − ∂ x u ( t , x ′ , 0 ) = γ | u | q ( t , x ′ , 0 ) , t > 0 , x ′ ∈ R n − 1 where p = 1 + 2 n , q = 1 + 1 n and ε > 0 is small enough. We investigate the life span of solutions for λ , γ > 0. Also we study the global in time existence and large time asymptotic behavior of solutions in the case of λ , γ < 0 and ∫ R + n u 0 ( x ) d x > 0.

scholarly journals Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

2017 ◽  
Vol 2017 ◽  
pp. 1-21
Author(s):  
Fernando Bernal-Vílchis ◽  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Pseudodifferential Operator ◽  
Critical Case ◽  
Large Time ◽  
Asymptotic Behavior Of Solutions ◽  
The Cauchy Problem ◽  
Time Existence ◽  
Time Asymptotic Behavior

We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂x∂tu-b/3∂x3u-∂xKu3=au, t,x∈R2,  u0,x=u0x, x∈R, where ab>0. Define ξ0=27a/b1/4. Suppose that K is a pseudodifferential operator with a symbol K^ξ such that K^±ξ0=0, Im K^ξ=0, and K^ξ≤C. For example, we can take K^ξ=ξ2-ξ02/ξ2+1. We prove the global in time existence and the large time asymptotic behavior of solutions.

scholarly journals Large Time Existence for Thin Vibrating Plates

2011 ◽  
Vol 36 (12) ◽  
pp. 2062-2102 ◽  
Author(s):  
Helmut Abels ◽  
Maria Giovanna Mora ◽  
Stefan Müller
Keyword(s):  
Large Time ◽  
Vibrating Plates ◽  
Time Existence

On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory

1988 ◽  
Vol 55 (1) ◽  
pp. 213-219 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Three Dimensional ◽  
Critical Depth ◽  
Transient Phenomena ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Dimensional Surface

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.

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