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

Gershon Kresin; Vladimir Maz'ya

doi:10.1080/17476933.2020.1797707

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

Gershon Kresin, Vladimir Maz'ya

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	945-963
Number of pages	19
Journal	Complex Variables and Elliptic Equations
Volume	66
Issue number	6-7
DOIs	https://doi.org/10.1080/17476933.2020.1797707
State	Published - 2021

Keywords

35A23
Cauchy problem
Primary 35K45
Secondary 47A30
directional derivative of a vector-valued function
sharp pointwise estimates
weakly coupled parabolic system

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10.1080/17476933.2020.1797707

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abstract = "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.",

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T1 - Sharp pointwise estimates for solutions of weakly coupled second-order parabolic system in a layer

AU - Kresin, Gershon

AU - Maz'ya, Vladimir

PY - 2021

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AB - 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.

KW - 35A23

KW - Cauchy problem

KW - Primary 35K45

KW - Secondary 47A30

KW - directional derivative of a vector-valued function

KW - sharp pointwise estimates

KW - weakly coupled parabolic system

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SN - 1747-6933

VL - 66

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JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 6-7

ER -

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

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