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Information × Registration Number 0217U007475, 0115U000136 , R & D reports Title Metric spaces, functions and operators harmonic analysis , singular and nonclassical problems for differential equations popup.stage_title Head Shishkov Andrey Evgenievich, Доктор фізико-математичних наук Registration Date 15-01-2018 Organization Donetsk State University popup.description2 The Keller-Osserman estimates and Harnack's inequality were obtained for the evolution p-Laplacian equation, for anisotropic porous medium equation, including equations with gradient absorption terms, and also for double-phase elliptic equations with absorption potential.The sufficient condition for removability of isolated singularities were proved for anisotropic porous medium equation with gradient absorption terms, local boundedness and continuous of weak solutions were proved for anisotropic porous medium equation. A qualitative analysis of the quasilinear differential equations of diffusion-strong nonlinear absorption structure, boundary and initial problems for them with supersingular data is carried out. The precise conditions were established that guarantee the localization of the domain of solutions singularity in the neighborhood of the parabolic boundary of the domain. The theory of scattering for self-adjoint and non-self-adjoint extensions of symmetric operator with equal (possibly infinite) defective numbers has been carried out by way of functional model and the theory of boundary triples. This construction was applied to the analysis of the scattering problem on a noncompact quantum graph, which allowed us to obtain a scattering matrix in explicit form. Product Description popup.authors Буряченко Катерина Олександрівна Войтович Михайло Володимирович Деркач Володимир Олександрович Ковальов Іван Михайлович Кудрич Юлія Сергіївна Нейман Євген Вікторович Скрипнік Ігор Ігорович Сухорукова Олена Олегівна Трофименко Віра Дмитрівна Трофименко Ольга Дмитрівна Шань Марія Олексіївна popup.nrat_date 2020-04-02 Close