Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations

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Volume 11, Issue 4

Changxing Miao & Yonggeng Gu

J. Part. Diff. Eq., 11 (1998), pp. 301-312.

Published online: 1998-11

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Abstract

In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space.

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Multipliers parabolic type equations Cauchy problem initial boundary value problem space-time estimate

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@Article{JPDE-11-301, author = {Changxing Miao and Yonggeng Gu }, title = {Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations}, journal = {Journal of Partial Differential Equations}, year = {1998}, volume = {11}, number = {4}, pages = {301--312}, abstract = { In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5572.html} }

TY - JOUR T1 - Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations AU - Changxing Miao & Yonggeng Gu JO - Journal of Partial Differential Equations VL - 4 SP - 301 EP - 312 PY - 1998 DA - 1998/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5572.html KW - Multipliers KW - parabolic type equations KW - Cauchy problem KW - initial boundary value problem KW - space-time estimate AB - In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space.

Changxing Miao and Yonggeng Gu . (1998). Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations. Journal of Partial Differential Equations. 11 (4). 301-312. doi:

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