This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div｜u｜p-2um）＋｜x｜α uq ,（x,t）∈RN×（0,t）,where N ≥ 1, 1 〈 p 〈 2, m 〉 max（0,3 -p/N} satisfyi...This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div｜u｜p-2um）＋｜x｜α uq ,（x,t）∈RN×（0,t）,where N ≥ 1, 1 〈 p 〈 2, m 〉 max（0,3 -p/N} satisfying 2 〈 p＋m 〈 3, q 〉 1, and（α 〉 N（3 - p - m） - p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.展开更多
Carbon source is a critical constraint on nutrient removal in domestic wastewater treatment.However,the functions of particulate organic matter（POM） and some organics with high molecular weight（HMW） are overlooked...Carbon source is a critical constraint on nutrient removal in domestic wastewater treatment.However,the functions of particulate organic matter（POM） and some organics with high molecular weight（HMW） are overlooked in the conventional process,as they cannot be directly assimilated into cells during microbial metabolism.This further aggravates the problem of carbon source shortage and thus affects the effluent quality.Therefore,to better characterize organic matter（OM） based MW distribution,microfiltration/ultrafiltration/nanofiltration（MF/UF/NF） membranes were used in parallel to fractionate OM,which obtained seven fractions.Hydrolysis acidification（HA） was adopted to manipulate the MW distribution of dissolved organic matter（DOM） and further explore the correlation between molecular size and biodegradability.Results showed that HA pretreatment of wastewater not only promoted transformation from POM to DOM,but also boosted biodegradability.After 8 hr of HA,the concentration of dissolved organic carbon（DOC） increased by 65%,from the initial value of20.25 to 33.48 mg/L,and the biodegradability index（BOD5（biochemical oxygen demand）/SCOD（soluble chemical oxygen demand）） increased from 0.52 to 0.74.Using MW distribution analysis and composition optimization,a new understanding on the characteristics of organics in wastewater was obtained,which is of importance to solving low C/N wastewater treatment in engineering practice.展开更多
基金partially supported by the Doctor Start-up Funding and Natural Science Foundation of Chongqing University of Posts and Telecommunications(A2014-25 and A2014-106)partially supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1500403)+3 种基金the Basic and Advanced Research Project of CQCSTC(cstc2015jcyj A00008)partially supported by NSFC(11371384),partially supported by NSFC(11426047)the Basic and Advanced Research Project of CQCSTC(cstc2014jcyj A00040)the Research Fund of Chongqing Technology and Business University(2014-56-11)
文摘This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div｜u｜p-2um）＋｜x｜α uq ,（x,t）∈RN×（0,t）,where N ≥ 1, 1 〈 p 〈 2, m 〉 max（0,3 -p/N} satisfying 2 〈 p＋m 〈 3, q 〉 1, and（α 〉 N（3 - p - m） - p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.
基金supported by the Jiangsu Water Resources Protection Project(No.2015005)the National High-Tech Research Program(863)of China(No.2012AA063302)the Fundamental Research Funds for Central Universities(No.2013/B14020391)
文摘Carbon source is a critical constraint on nutrient removal in domestic wastewater treatment.However,the functions of particulate organic matter（POM） and some organics with high molecular weight（HMW） are overlooked in the conventional process,as they cannot be directly assimilated into cells during microbial metabolism.This further aggravates the problem of carbon source shortage and thus affects the effluent quality.Therefore,to better characterize organic matter（OM） based MW distribution,microfiltration/ultrafiltration/nanofiltration（MF/UF/NF） membranes were used in parallel to fractionate OM,which obtained seven fractions.Hydrolysis acidification（HA） was adopted to manipulate the MW distribution of dissolved organic matter（DOM） and further explore the correlation between molecular size and biodegradability.Results showed that HA pretreatment of wastewater not only promoted transformation from POM to DOM,but also boosted biodegradability.After 8 hr of HA,the concentration of dissolved organic carbon（DOC） increased by 65%,from the initial value of20.25 to 33.48 mg/L,and the biodegradability index（BOD5（biochemical oxygen demand）/SCOD（soluble chemical oxygen demand）） increased from 0.52 to 0.74.Using MW distribution analysis and composition optimization,a new understanding on the characteristics of organics in wastewater was obtained,which is of importance to solving low C/N wastewater treatment in engineering practice.
