Addition of Lower Order Terms to Weakly Hyperbolic Operators with Preservation of Their Type of Hyperbolicit
- Авторлар: Ghazaryan H.1,2, Margaryan V.1
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Мекемелер:
- Russian-Armenian University
- Institute of Mathematics
- Шығарылым: Том 40, № 8 (2019)
- Беттер: 1069-1078
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205174
- DOI: https://doi.org/10.1134/S1995080219080092
- ID: 205174
Дәйексөз келтіру
Аннотация
For an m-homogeneous hyperbolic (with respect to the vector N) operator Pm, and a weight function g: 1) we find the conditions on the lower order terms {Q}, operators {Pm(D) + Q(D)} to become g-hyperbolic with respect to any vector N1 from a neighborhood O(N) of the vector N, 2) we show that the operators obtained by adding lower order terms have fundamental solutions whose supports are in the cone from upper half-space \(\overline {{H_N}} : = \{ (x,N) \ge 0\} \), 3) we show that if P(D):= (Pm + Q)(D), f ∈ Gℜ (where Gℜ is some Gevrey type space) and supp f ⊂ HN:= {(x, N) > 0}, the equation P(D)u = f has a solution u ∈ Gℜ such that supp \(u \subset \overline {{H_N}} \).
Авторлар туралы
H. Ghazaryan
Russian-Armenian University; Institute of Mathematics
Хат алмасуға жауапты Автор.
Email: haikghazaryan@mail.ru
Армения, Yerevan, 0051; Yerevan, 0019
V. Margaryan
Russian-Armenian University
Хат алмасуға жауапты Автор.
Email: vachagan.margaryan@yahoo.com
Армения, Yerevan, 0051