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: Research Article On Initial Boundary Value Problems with Equivalued Surface for Nonlinear Parabolic Equations Fengquan Li | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 739097 23 pages doi 2009 739097 Research Article On Initial Boundary Value Problems with Equivalued Surface for Nonlinear Parabolic Equations Fengquan Li Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Correspondence should be addressed to Fengquan Li fqli@ Received 6 January 2009 Revised 12 March 2009 Accepted 22 May 2009 Recommended by Sandro Salsa We will use the concept of renormalized solution to initial boundary value problems with equivalued surface for nonlinear parabolic equations discuss the existence and uniqueness of renormalized solution and give the relation between renormalized solutions and weak solutions. Copyright 2009 Fengquan Li. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let Q c RnN 2 be a bounded domain with Lipschitz boundary dQ r. T is a fixed positive constant Q Q X 0 T . We consider the following nonlinear parabolic boundary value problems with equivalued surface du N d du dt - Xdx aij x u j f M in Q u C t a function of t to be determined on r X 0 T f x ds A f r dnL V e 0 T u x 0 0 in Q P where f e L2 Q and A e L2 0 T n n1 . nN denotes the unit outward normal vector on r and du N . . du aij x u ni. dnL j1 dx 2 Boundary Value Problems There are many concrete physical sources for problem F for example in the petroleum exploitation u denotes the oil pressure and A t is the rate of total oil flux per unit length of the well at the time t in the combustion theory u denotes the temperature for any fixed time t the temperature distribution on the boundary is a constant to be determined while the total heat A i through the boundary is given cf. 1-7 . For linear equations the existence uniqueness of solution to the .