A priori estimates of global solutions of superlinear parabolic problems without variational structure

2003 ◽  
Vol 9 (5) ◽  
pp. 1277-1292 ◽  
Author(s):  
Pavol Quittner ◽  
◽  
Philippe Souplet ◽  
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Global Solutions ◽  
Parabolic Problems ◽  
Priori Estimates ◽  
Variational Structure

GLOBAL EXISTENCE AND ASYMPTOTIC STABILITY FOR THE NONLINEAR AND GENERALIZED DAMPED EXTENSIBLE PLATE EQUATION

2004 ◽  
Vol 06 (05) ◽  
pp. 705-731 ◽  
Author(s):  
M. M. CAVALCANTI ◽  
V. N. DOMINGOS CAVALCANTI ◽  
J. A. SORIANO
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Global Solutions ◽  
Finite Measure ◽  
Decay Rates ◽  
Beam Equation ◽  
Uniform Decay ◽  
Open Set ◽  
Priori Estimates ◽  
The Fixed Point Theorem

The nonlinear and damped extensible plate (or beam) equation is considered [Formula: see text] where Ω is any bounded or unbounded open set of Rn, α>0 and f, g are power like functions. The existence of global solutions is proved by means of the Fixed Point Theorem and continuity arguments. To this end we avoid handling the nonlinearity M(∫Ω|∇u|2dx) in the a priori estimates of energy. Furthermore, uniform decay rates of the energy are also obtained by making use of the perturbed energy method for domains with finite measure.

scholarly journals ASYMPTOTIC BEHAVIOR OF GLOBAL SOLUTIONS TO A MODEL OF CELL INVASION

2010 ◽  
Vol 20 (09) ◽  
pp. 1721-1758 ◽  
Author(s):  
GABRIELA LIŢCANU ◽  
CRISTIAN MORALES-RODRIGO
Keyword(s):  
Asymptotic Behavior ◽  
Cell Invasion ◽  
A Priori Estimates ◽  
A Priori ◽  
Global Solutions ◽  
Coupled System ◽  
Regularity Properties ◽  
Priori Estimates ◽  
Degradative Enzymes ◽  
Key Events

In this paper, we analyze a mathematical model focusing on key events of the cell invasion process. The three equations of the corresponding coupled system describe the behavior of the invasive cells, the extracellular matrix and the degradative enzymes. We employ a fix-point method and a priori estimates to prove local and global existence, uniqueness and regularity properties of the solutions. Our approach enable us to find estimates that are uniform in time. This is essential in proving, in the last part of the paper, new results that establish the asymptotic behavior of the solutions.

A Priori Estimates for Some Classes of Difference Schemes

1996 ◽  
Vol 48 (2) ◽  
pp. 244-257 ◽  
Author(s):  
Nikolai Bakaev
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Difference Schemes ◽  
Parabolic Problems ◽  
Well Posedness ◽  
Lebesgue Spaces ◽  
New Approach ◽  
Priori Estimates

AbstractA new approach to the analysis of the well-posedness of difference parabolic problems is proposed, which is based on weaker assumptions than in earlier works. The results are applied to the study of multi-dimensional difference parabolic problems in mesh Lebesgue spaces.

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