Symmetrization and Mass Comparison for Degenerate Nonlinear Parabolic and Related Elliptic Equations

2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Juan Luis Vázquez
Keyword(s):  
Parabolic Equations ◽  
A Priori ◽  
Porous Medium Equation ◽  
Nonlinear Parabolic Equations ◽  
Detailed Knowledge ◽  
Medium Equation ◽  
Mass Comparison ◽  
Nonlinear Parabolic ◽  
Comparison Results ◽  
Special Solutions

AbstractWe consider the solutions to various nonlinear parabolic equations and their elliptic counterparts and prove comparison results based on two main tools, symmetrization and mass concentration comparison. The work focuses on equations like the porous medium equation, the filtration equation and the p-Laplacian equation. The results will be used in a companion work in combination with a detailed knowledge of special solutions to obtain sharp a priori bounds and decay estimates for wide classes of solutions of those equations.

Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak-spaces

2021 ◽  
Vol 8 (4) ◽  
pp. 584-600
Author(s):  
A. Aberqi ◽  
◽  
M. Elmassoudi ◽  
M. Hammoumi ◽  
◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Evolution Equations ◽  
Nonlinear Term ◽  
A Priori ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Evolution Equations ◽  
A Priori Error Estimate ◽  
Nonlinear Parabolic ◽  
Backward Euler ◽  
Internal Approximation

In this paper, a class of nonlinear evolution equations with damping arising in fluid dynamics and rheology is studied. The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth. The appropriate functional framework for such equations is the modularly Museilak–spaces. The existence and uniqueness of a weak solution are proved using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given.

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.

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