Global Existence and Asymptotic Stability for a Semilinear Hyperbolic Volterra Equation with Large Initial Data

1985 ◽  
Vol 16 (1) ◽  
pp. 110-134 ◽  
Author(s):  
William J. Hrusa
Keyword(s):  
Asymptotic Stability ◽  
Initial Data ◽  
Global Existence ◽  
Volterra Equation ◽  
Large Initial Data

scholarly journals Vanishing shear viscosity limit and boundary layer study for the planar MHD system

2019 ◽  
Vol 29 (06) ◽  
pp. 1139-1174 ◽  
Author(s):  
Xulong Qin ◽  
Tong Yang ◽  
Zheng-an Yao ◽  
Wenshu Zhou
Keyword(s):  
Boundary Layer ◽  
Initial Data ◽  
Global Existence ◽  
Shear Viscosity ◽  
Initial Boundary ◽  
Heat Conductivity Coefficient ◽  
Large Initial Data ◽  
Initial Boundary Problem ◽  
Viscosity Limit ◽  
Mhd System

We consider an initial boundary problem for the planar MHD system under the general condition on the heat conductivity coefficient that depends on both the temperature and the density. Firstly, the global existence of strong solution for large initial data is obtained, and then the limit of the vanishing shear viscosity is justified. In addition, the [Formula: see text] convergence rate is obtained together with the estimation on the thickness of the boundary layer.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO DRIFT-DIFFUSION SYSTEM WITH GENERALIZED DISSIPATION

2009 ◽  
Vol 19 (06) ◽  
pp. 939-967 ◽  
Author(s):  
TAKAYOSHI OGAWA ◽  
MASAKAZU YAMAMOTO
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Asymptotic Expansion ◽  
Initial Data ◽  
Global Existence ◽  
Asymptotic Behavior Of Solutions ◽  
Large Initial Data ◽  
Drift Diffusion ◽  
Nonlinear Parabolic ◽  
The Cauchy Problem

We show the global existence and asymptotic behavior of solutions for the Cauchy problem of a nonlinear parabolic and elliptic system arising from semiconductor model. Our system has generalized dissipation given by a fractional order of the Laplacian. It is shown that the time global existence and decay of the solutions to the equation with large initial data. We also show the asymptotic expansion of the solution up to the second terms as t → ∞.

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