THE EXPLICIT FORM OF THE FUNDAMENTAL SOLUTION OF ONE PSEUDO-DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS
Keywords:
pseudo-differential operator, fundamental solution, stable stochastic process.Abstract
We consider pseudo-differential equation of the form ut ′ = Au + ( a, B)u here a is a vector in R d , B is a pseudo-differential operator with symbol (i | λ | α −2 λ ) d and c > 0 , α ∈ (1,2] are fixed constants. The fundamental λ∈ R solution of this equation is constructed in the form of inverse Fourier transform. Some of its properties investigated.
References
1. Кочубей А.Н. Параболические псевдодифференциальные уравнения, гиперсингулярные интегралы и марковские процессы / А.Н. Кочубей // Известия АН СССР. – 1988. – 52(5). – С. 909-934.
2. Osypchuk M.M. On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations / M.M. Osypchuk // Carpathian Math. Publ. – 2015. – 7 (1).
2. Osypchuk M.M. On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations / M.M. Osypchuk // Carpathian Math. Publ. – 2015. – 7 (1).
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Published
2019-02-26
How to Cite
Бігун, Г. С., & Осипчук, М. М. (2019). THE EXPLICIT FORM OF THE FUNDAMENTAL SOLUTION OF ONE PSEUDO-DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(29), 123–131. Retrieved from https://www.pvntsh.nung.edu.ua/index.php/number/article/view/148
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Section
Mathematics and Mechanics
