We study the initial value problem for a nonlinear parabolic equation with singular integral-differential term. By means of a series of a priori estimations of the solutions to the problem andLeray-Schauder fixed poin...We study the initial value problem for a nonlinear parabolic equation with singular integral-differential term. By means of a series of a priori estimations of the solutions to the problem andLeray-Schauder fixed point principle, we demonstrate the existence and uniqueness theorems ofthe generalized and classical global solutions. Lastly, we discuss the asymptotic properties of thesolution as t tends to infinity.展开更多
We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space...We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.展开更多
文摘We study the initial value problem for a nonlinear parabolic equation with singular integral-differential term. By means of a series of a priori estimations of the solutions to the problem andLeray-Schauder fixed point principle, we demonstrate the existence and uniqueness theorems ofthe generalized and classical global solutions. Lastly, we discuss the asymptotic properties of thesolution as t tends to infinity.
基金Supported by the National Natural Science Foundation of China(11571093)the Natural Science Foundation of Jiangsu Education Commission China(19KJB110016)。
基金Supported by Ministry of Science of Republic Serbia
文摘We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.
