scholarly journals Global existence and asymptotic behavior for a generalized Boussinesq type equation without dissipation

2021 ◽  
Author(s):  
Guowei Liu ◽  
Wei Wang ◽  
Qiuju Xu
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Initial Data ◽  
Global Existence ◽  
Linear Group ◽  
Type Equation ◽  
Small Initial Data ◽  
Dispersive Estimate ◽  
The Cauchy Problem

In this paper, we study the Cauchy problem for a generalized Boussinesq type equation in $\mathbb{R}^n$. We establish a dispersive estimate for the linear group associated with the generalized Boussinesq type equation. As applications, the global existence, decay and scattering of solutions are established for small initial data.

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 → ∞.

Global Existence of Solution for Cauchy Problem of Two-Dimensional Boussinesq-Type Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Qingying Hu ◽  
Chenxia Zhang ◽  
Hongwei Zhang
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Initial Data ◽  
Global Existence ◽  
Exponential Growth ◽  
Type Equation ◽  
Global Weak Solution ◽  
Existence Of Solution ◽  
Two Dimensional ◽  
The Cauchy Problem

In this paper, we consider the Cauchy problem of two-dimensional Boussinesq-type equations utt-Δu-Δutt+Δ2u=Δfu. Under the assumptions that fu is a function with exponential growth at infinity and under some assumptions on the initial data, we prove the existence of global weak solution.

Singularities of solutions for first order quasilinear hyperbolic systems

1983 ◽  
Vol 94 (1-2) ◽  
pp. 137-147 ◽  
Author(s):  
Lee Da-tsin(Li Ta-tsien) ◽  
Shi Jia-hong
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Hyperbolic Systems ◽  
Smooth Solutions ◽  
Small Initial Data ◽  
Quasilinear Hyperbolic Systems ◽  
First Order ◽  
Global Smooth Solutions ◽  
The Cauchy Problem

SynopsisIn this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

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