Local boundedness of weak solutions for nonlinear parabolic problem with p (x) -growth

Ning Pan; Yongqiang Fu

doi:10.1155/2010/163269

Local boundedness of weak solutions for nonlinear parabolic problem with p (x) -growth

Ning Pan^*
, Yongqiang Fu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

9 Scopus citations

Abstract

We study the nonlinear parabolic problem with p (x) -growth conditions in the space W^{1, x}L^{p (x)} (Q) and give a local boundedness theorem of weak solutions for the following equation ( u / t) + A (u) = 0, where A (u) = - div a (x, t, u, δ u) + a 0 (x, t, u, δ u), a (x, t, u, δ u) and a 0 (x, t, u, δ u) satisfy p (x) -growth conditions with respect to u and δ u.

Original language	English
Article number	163269
Journal	Journal of Inequalities and Applications
Volume	2010
DOIs	https://doi.org/10.1155/2010/163269
State	Published - 2010

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abstract = "We study the nonlinear parabolic problem with p (x) -growth conditions in the space W1, xLp (x) (Q) and give a local boundedness theorem of weak solutions for the following equation ( u / t) + A (u) = 0, where A (u) = - div a (x, t, u, δ u) + a 0 (x, t, u, δ u), a (x, t, u, δ u) and a 0 (x, t, u, δ u) satisfy p (x) -growth conditions with respect to u and δ u.",

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AB - We study the nonlinear parabolic problem with p (x) -growth conditions in the space W1, xLp (x) (Q) and give a local boundedness theorem of weak solutions for the following equation ( u / t) + A (u) = 0, where A (u) = - div a (x, t, u, δ u) + a 0 (x, t, u, δ u), a (x, t, u, δ u) and a 0 (x, t, u, δ u) satisfy p (x) -growth conditions with respect to u and δ u.

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ER -

Local boundedness of weak solutions for nonlinear parabolic problem with p (x) -growth

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