A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations
Коэффициентi үзiлiстi жылуөткiзгiштiк теңдеу үшiн Коши есебi шешiмiнiң соболев класындағы априорлық бағасы
Априорная оценка решения задачи Коши для вырождающегося уравнения теплопроводности с разрывными коэффициентами в соболевских классах
Koilyshov U.K. Beisenbaeva K.A. Zhapparova S.D.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#107Issue 359 - 69 pp.
Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors. Conjugation problems for time-degenerate equations of the parabolic type with discontinuous coefficients are practically not studied. In this work, in an n-dimensional space, a conjugation problem is considered for a heat equation with discontinuous coefficients which degenerates at the initial moment of time. A fundamental solution to the set problem has been constructed and estimates of its derivatives have been found. With the help of these estimates, in the Sobolev classes, the estimate of the solution to the set problem was obtained.
conjugation problem , degenerating equations , discontinuous coefficients , heat equation
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
Academy of Logistics and Transport, Almaty, Kazakhstan
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modelling
Academy of Logistics and Transport
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026