Sharp pointwise estimates for solutions of weakly coupled second-order parabolic system in a layer

We deal with m-component vector-valued solutions to the Cauchy problem for a linear both homogeneous and nonhomogeneous weakly coupled second-order parabolic system in the layer (Formula presented.). We assume that coefficients of the system are real and depending only on t, (Formula presented.) and (Formula presented.). The homogeneous system is considered with initial data in (Formula presented.), (Formula presented.). For the nonhomogeneous system we suppose that the initial function is equal to zero and the right-hand side belongs to (Formula presented.), (Formula presented.). Explicit formulas for the sharp coefficients in pointwise estimates for solutions to these problems and their directional derivative are obtained. © 2020 Informa UK Limited, trading as Taylor & Francis Group.

Авторы
Kresin G.1 , Maz'ya V. 2, 3, 4
Язык
Английский
Статус
Опубликовано
Год
2020
Организации
  • 1 Department of Mathematics, Ariel University, Ariel, Israel
  • 2 Department of Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom
  • 3 Department of Mathematics, Linköping University, Linköping, Sweden
  • 4 RUDN University, Moscow, Russian Federation
Ключевые слова
35A23; Cauchy problem; directional derivative of a vector-valued function; Primary 35K45; Secondary 47A30; sharp pointwise estimates; weakly coupled parabolic system
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/65494/