Determining of three unknown functions of a semilinear ultraparabolic equation

2020 ◽  
Vol 44 (1) ◽  
pp. 617-633
Author(s):  
Nataliya Protsakh
Keyword(s):  
Ultraparabolic Equation

scholarly journals THE Cα REGULARITY OF A CLASS OF ULTRAPARABOLIC EQUATIONS

2011 ◽  
Vol 13 (03) ◽  
pp. 375-387
Author(s):  
LIQUN ZHANG
Keyword(s):  
Weak Solutions ◽  
High Dimensional ◽  
Ultraparabolic Equation ◽  
Measurable Coefficients ◽  
Ultraparabolic Equations ◽  
Regularity Results

We prove the Cα regularity for weak solutions to a class of ultraparabolic equation, with measurable coefficients. The result generalized our recent Cα regularity results of Prandtl's system to high dimensional cases.

THE MOSER'S ITERATIVE METHOD FOR A CLASS OF ULTRAPARABOLIC EQUATIONS

2004 ◽  
Vol 06 (03) ◽  
pp. 395-417 ◽  
Author(s):  
ANDREA PASCUCCI ◽  
SERGIO POLIDORO
Keyword(s):  
Iterative Method ◽  
Weak Solutions ◽  
Ad Hoc ◽  
Iterative Scheme ◽  
Sobolev Type ◽  
Ultraparabolic Equation ◽  
Measurable Coefficients ◽  
Ultraparabolic Equations ◽  
Bounded Functions

We adapt the iterative scheme by Moser, to prove that the weak solutions to an ultraparabolic equation, with measurable coefficients, are locally bounded functions. Due to the strong degeneracy of the equation, our method differs from the classical one in that it is based on some ad hoc Sobolev type inequalities for solutions.

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