ultraparabolic equations
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2020 ◽  
Vol 12 (1) ◽  
pp. 79-87
Author(s):  
G.P. Malytska ◽  
I.V. Burtnyak

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.





Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 286
Author(s):  
Michael Marcozzi

We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.











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