A new high‐order weighted essentially non‐oscillatory scheme for non‐linear degenerate parabolic equations

2020 ◽  
Author(s):  
Rooholah Abedian
Keyword(s):  
Parabolic Equations ◽  
High Order ◽  
Degenerate Parabolic Equations ◽  
Non Linear ◽  
Degenerate Parabolic ◽  
Linear Degenerate

scholarly journals Construction of the fundamental solution of a class of degenerate parabolic equations of high order

2020 ◽  
Vol 12 (1) ◽  
pp. 79-87
Author(s):  
G.P. Malytska ◽  
I.V. Burtnyak
Keyword(s):  
Fundamental Solution ◽  
Green's Function ◽  
Parabolic Equations ◽  
Arbitrary Number ◽  
High Order ◽  
Exponential Estimate ◽  
Degenerate Parabolic Equations ◽  
Kolmogorov Equations ◽  
Ultraparabolic Equations ◽  
Degenerate Parabolic

In the article, using the modified Levy method, a Green's function for a class of ultraparabolic equations of high order with an arbitrary number of parabolic degeneration groups is constructed. The modified Levy method is developed for high-order Kolmogorov equations with coefficients depending on all variables, while the frozen point, which is a parametrix, is chosen so that an exponential estimate of the fundamental solution and its derivatives is conveniently used.

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