scholarly journals Global solutions in the critical Sobolev space for the wave equations with nonlinearity of exponential growth

1999 ◽  
Vol 231 (3) ◽  
pp. 479-487 ◽  
Author(s):  
M. Nakamura ◽  
T. Ozawa
Keyword(s):  
Sobolev Space ◽  
Exponential Growth ◽  
Wave Equations ◽  
Global Solutions ◽  
Critical Sobolev Space

Adams Type Inequality and Application for a Class of Polyharmonic Equations with Critical Growth

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
João Marcos do Ó ◽  
Abiel Costa Macedo
Keyword(s):  
Sobolev Space ◽  
Exponential Growth ◽  
Type Inequality ◽  
Critical Growth ◽  
Polyharmonic Equations ◽  
Critical Exponential Growth

AbstractIn this paper we give a new Adams type inequality for the Sobolev space W(−Δ)where the nonlinearity is “superlinear” and has critical exponential growth at infinite.

Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space

2019 ◽  
Vol 169 (1) ◽  
pp. 199-215
Author(s):  
Jaewook Ahn ◽  
Jihoon Lee
Keyword(s):  
Sobolev Space ◽  
Small Data ◽  
Critical Sobolev Space

scholarly journals Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun Ye
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equations ◽  
Decay Estimate ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Initial Boundary Value ◽  
Nonlinear Degenerate

This paper studies the existence of global solutions to the initial-boundary value problem for some nonlinear degenerate wave equations by means of compactness method and the potential well idea. Meanwhile, we investigate the decay estimate of the energy of the global solutions to this problem by using a difference inequality.

Remarks on Gagliardo–Nirenberg type inequality with critical Sobolev space and BMO

2007 ◽  
Vol 259 (4) ◽  
pp. 935-950 ◽  
Author(s):  
Hideo Kozono ◽  
Hidemitsu Wadade
Keyword(s):  
Sobolev Space ◽  
Type Inequality ◽  
Critical Sobolev Space
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