Continuity of solutions of a singular parabolic equation

1983 ◽  
Vol 7 (4) ◽  
pp. 387-409 ◽  
Author(s):  
Paul E. Sacks
Keyword(s):  
Parabolic Equation ◽  
Singular Parabolic Equation ◽  
Continuity Of Solutions

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

Local Hölder regularity for a doubly singular PDE

2018 ◽  
Vol 22 (03) ◽  
pp. 1850054
Author(s):  
Eurica Henriques
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Iteration Method ◽  
Hölder Continuity ◽  
Hölder Regularity ◽  
Holder Continuity ◽  
Singular Parabolic Equation ◽  
Local Hölder Continuity ◽  
Singular Pde ◽  
Bounded Weak Solutions

We establish the local Hölder continuity for the nonnegative bounded weak solutions of a certain doubly singular parabolic equation. The proof involves the method of intrinsic scaling and the parabolic version of De Giorgi’s iteration method.

scholarly journals On the dynamics of a strongly singular parabolic equation

2015 ◽  
Vol 421 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Georgios P. Trachanas ◽  
Nikolaos B. Zographopoulos
Keyword(s):  
Parabolic Equation ◽  
Singular Parabolic Equation

scholarly journals Existence and stabilization results for a singular parabolic equation involving the fractional Laplacian

2019 ◽  
Vol 12 (2) ◽  
pp. 311-337
Author(s):  
Jacques Giacomoni ◽  
◽  
Tuhina Mukherjee ◽  
Konijeti Sreenadh ◽  
Keyword(s):  
Parabolic Equation ◽  
Fractional Laplacian ◽  
Singular Parabolic Equation

scholarly journals Blow-up for a degenerate and singular parabolic equation with a nonlocal source

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Nitithorn Sukwong ◽  
Panumart Sawangtong ◽  
Sanoe Koonprasert ◽  
Wannika Sawangtong
Keyword(s):  
Parabolic Equation ◽  
Blow Up ◽  
Nonlocal Source ◽  
Singular Parabolic Equation
Sign in / Sign up

Export Citation Format

Share Document