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báo cáo hóa học:" L^{\infty} estimates of solutions for the quasilinear parabolic equation with nonlinear gradient term and L^1 data"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: L^{\infty} estimates of solutions for the quasilinear parabolic equation with nonlinear gradient term and L^1 data | Boundary Value Problems SpringerOpen0 This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text HTML versions will be made available soon. LA infty estimates of solutions for the quasilinear parabolic equation with nonlinear gradient term and LA1 data Boundary Value Problems 2012 2012 19 doi 10.1186 1687-2770-2012-19 Caisheng Chen cshengchen@hhu.edu.cn Fei Yang yangfei3022@163.com Zunfu Yang qq348450449@163.com ISSN 1687-2770 Article type Research Submission date 10 August 2011 Acceptance date 15 February 2012 Publication date 15 February 2012 Article URL http www.boundaryvalueproblems.com content 2012 1 19 This peer-reviewed article was published immediately upon acceptance. It can be downloaded printed and distributed freely for any purposes see copyright notice below . For information about publishing your research in Boundary Value Problems go to http www.boundaryvalueproblems.com authors instructions For information about other SpringerOpen publications go to http www.springeropen.com 2012 Chen et al. licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. L1 estimates of solutions for the quasilinear parabolic equation with nonlinear gradient term and L1 data Caisheng Chen1 Fei Yang2 and Zunfu Yang3 College of Science Hohai University Nanjing 210098 P. R. China Corresponding author cshengchen@hhu.edu.cn Email addresses FY yangfei3022@163.com ZY qq348450449@163.com Abstract In this article we study the quasilinear parabolic problem ut div Vu mVu u u 2 Vu ợ u u 2 Vu p g u x 2 t 0 u x 0 u0 x x 2 u x t 0 x 2 Ỡ t 0 0-1 where is a bounded domain in Rw m 0 and g u satisfies g u K u V with 0 m. By the Moser s technique we prove that if a 3 1 0 p q 1 q m 2 p a q 3 there exists a weak .