scholarly journals Existence and Nonexistence of Global Solutions of a Fully Nonlinear Parabolic Equation

2013 ◽  
Vol 03 (01) ◽  
pp. 20-23
Author(s):  
Zhihao Ge
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Global Solutions ◽  
Fully Nonlinear ◽  
Nonlinear Parabolic ◽  
Existence And Nonexistence

scholarly journals Regularity for the fully nonlinear parabolic thin obstacle problem

2021 ◽  
pp. 2150011
Author(s):  
Georgiana Chatzigeorgiou
Keyword(s):  
Parabolic Equation ◽  
Viscosity Solution ◽  
Nonlinear Parabolic Equation ◽  
Obstacle Problem ◽  
Elliptic Case ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Nonlinear Parabolic ◽  
Parabolic Case ◽  
Thin Obstacle

We prove [Formula: see text] regularity (in the parabolic sense) for the viscosity solution of a boundary obstacle problem with a fully nonlinear parabolic equation in the interior. Following the method which was first introduced for the harmonic case by L. Caffarelli in 1979, we extend the results of I. Athanasopoulos (1982) who studied the linear parabolic case and the results of E. Milakis and L. Silvestre (2008) who treated the fully nonlinear elliptic case.

scholarly journals Mathematical modeling of double nonlinear problem of reaction diffusion in not divergent form with a source and variable density

2021 ◽  
Vol 2131 (3) ◽  
pp. 032043
Author(s):  
M Aripov ◽  
A S Matyakubov ◽  
J O Khasanov ◽  
M M Bobokandov
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Variable Density ◽  
Divergence Form ◽  
Cross Diffusion ◽  
Nonlinear Parabolic ◽  
The Cauchy Problem

Abstract In this paper the properties of solutions of nonlinear parabolic equation not in divergence form | x | − 1 ∂ u ∂ t = u q ∂ ∂ x ( | x | n u m − 1 | ∂ u k ∂ x | p − 2 ∂ u ∂ x ) + | x | − 1 u β are studied. Depending on values of the numerical parameters and the initial value, the existence of the global solutions of the Cauchy problem is proved. Constructed asymptotic representation of self-similar solutions of nonlinear parabolic equation not in divergence form, depending on the value in the equation of the numerical parameters necessary and sufficient signs of their existence. The compactly supported solution of the Cauchy problem for a cross-diffusion parabolic equation not in divergence form with a source and a variable density is obtained.

scholarly journals GLOBAL AND NON-GLOBAL SOLUTIONS OF A NONLINEAR PARABOLIC EQUATION

2005 ◽  
Vol 9 (2) ◽  
pp. 187-200
Author(s):  
Jong-Shenq Guo ◽  
Yung-Jen Lin Guo ◽  
Chi-Jen Wang
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Global Solutions ◽  
Nonlinear Parabolic
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