tailieunhanh - báo cáo hóa học: " Weak solutions of functional differential inequalities with first-order partial derivatives"

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: Weak solutions of functional differential inequalities with first-order partial derivatives | Kamont Journal of Inequalities and Applications 2011 2011 15 http content 2011 1 15 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Weak solutions of functional differential inequalities with first-order partial derivatives Zdzislaw Kamont Correspondence Zdzislaw. Kamont@ Institute of Mathematics University of Gdansk Wit Stwosz Street 57 80-952 Gdansk Poland SpringerOpen0 Abstract The article deals with functional differential inequalities generated by the Cauchy problem for nonlinear first-order partial functional differential equations. The unknown function is the functional variable in equation and inequalities and the partial derivatives appear in a classical sense. Theorems on weak solutions to functional differential inequalities are presented. Moreover a comparison theorem gives an estimate for functions of several variables by means of functions of one variable which are solutions of ordinary differential equations or inequalities. It is shown that there are solutions of initial problems defined on the Haar pyramid. Mathematics Subject Classification 35R10 35R45. Keywords Functional differential inequalities Haar pyramid Comparison theorems Weak solutions of initial problems 1 Introduction Two types of results on first-order partial differential or functional differential equations are taken into considerations in the literature. Theorems of the first type deal with initial problems which are local or global with respect to spatial variables while the second one are concerned with initial boundary value problems. We are interested in results of the first type. More precisely we consider initial problems which are local with respect to spatial variables. Then the Haar pyramid is a natural domain on which solutions of differential or functional differential equations or inequalities are considered. Hyperbolic differential inequalities corresponding to initial .