A Priori Estimates for Fully Nonlinear Parabolic Equations

2012 ◽  
Vol 2013 (17) ◽  
pp. 3857-3877 ◽  
Author(s):  
Guji Tian ◽  
Xu-Jia Wang
Keyword(s):  
Parabolic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Nonlinear Parabolic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Parabolic ◽  
Priori Estimates

XXII.—A Priori Estimates and Nonlinear Parabolic Equations of Arbitrary Order

1972 ◽  
Vol 69 (4) ◽  
pp. 287-293
Author(s):  
D. E. Edmunds ◽  
C. A. Stuart
Keyword(s):  
Parabolic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Parabolic Equations ◽  
Linear Parabolic Equation ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Initial Boundary Value

SynopsisIn this paper it is shown that the question of the existence of a classical solution of the first initial-boundary value problem for a non-linear parabolic equation may be reduced to the problem of the derivation of suitable a priori bounds.

scholarly journals Bounded Solutions to Nonlinear Parabolic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Jaouad Igbida
Keyword(s):  
Parabolic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Nonlinear Parabolic Equations ◽  
Bounded Solutions ◽  
Test Function ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Compactness Arguments ◽  
Test Function Method

We deal with existence results for nonlinear parabolic equations with general quadratic gradient terms and with absorption term which depend on the solution. We note that no boundedness is assumed on the data of the problem. We prove an existence result of distributional solution via test-function method. A priori estimates and compactness arguments are our main ingredient; the method of sub-supersolution does not apply her.

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