scholarly journals Uniqueness of Piecewise Smooth Weak Solutions of Multidimensional Degenerate Parabolic Equations

1997 ◽  
Vol 210 (2) ◽  
pp. 598-608 ◽  
Author(s):  
Tamir Tassa
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Piecewise Smooth ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

scholarly journals Decreasing of the L^1 norm and mass conservation for Porous Medium Equations with advection

2018 ◽  
Vol 4 (2) ◽  
pp. 67-77
Author(s):  
Nicolau Matiel Lunardi Diehl ◽  
Lucinéia Fabris
Keyword(s):  
Cauchy Problem ◽  
Porous Medium ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Mass Conservation ◽  
Degenerate Parabolic Equations ◽  
Conservation Property ◽  
The Cauchy Problem ◽  
Porous Medium Equations ◽  
Degenerate Parabolic

In this paper, we show that the $L^1$ norm of the bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the formu_t + div f(x,t,u) = div(|u|^{\alpha}\nabla u),   x \in R^n , t > 0,where \alpha > 0 is constant, decrease, under fairly broad conditions in advection flow f. In addition, we derive the mass conservation property for positive (or negative) solutions.

scholarly journals Decreasing of the L^1 norm and mass conservation for Porous Medium Equations with advection

2018 ◽  
Vol 4 (2) ◽  
pp. 67-77
Author(s):  
Nicolau Matiel Lunardi Diehl ◽  
Lucinéia Fabris
Keyword(s):  
Cauchy Problem ◽  
Porous Medium ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Mass Conservation ◽  
Degenerate Parabolic Equations ◽  
Conservation Property ◽  
The Cauchy Problem ◽  
Porous Medium Equations ◽  
Degenerate Parabolic

In this paper, we show that the $L^1$ norm of the bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the formu_t + div f(x,t,u) = div(|u|^{\alpha}\nabla u),   x \in R^n , t > 0,where \alpha > 0 is constant, decrease, under fairly broad conditions in advection flow f. In addition, we derive the mass conservation property for positive (or negative) solutions.

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