Search

Your search keyword '"Zhou, Shulin"' showing total 10 results
Start Over Author "Zhou, Shulin" Topic uniqueness
10 results on '"Zhou, Shulin"'

4. Blow-up of porous medium equations with variable source power

Author

Xie Yuancheng, Zhou Shulin, and Zheng Zhi

Subjects
Discrete mathematics, Variable source, General Mathematics, Bounded function, Domain (ring theory), Initial value problem, Uniqueness, Space (mathematics), Spatial domain, Critical exponent, Mathematics
Abstract

In this paper, we study the blow-up and/or global existence of the following porous medium equation with variable source power, u t =Δ u m + u p ( x ) , in Ω×(0, T ), where Ω is either a bounded domain or the whole space R N , and p ( x ) is a positive and continuous bounded function defined in Ω satisfying 0 p - =inf p ( x )≤ p ( x )≤ p + =sup p ( x ) p ( x ) and the structure of spatial domain Ω. Roughly speaking, for the Cauchy problem, if p ( x )≤1, uniqueness of the solutions might not hold, and all nontrivial solutions exist globally. If p + > m , there are blow-up solutions. If 1 p ( x )≤ m +2/ N , every nontrivial solution blows up. If p ( x )> m +2/ N , there exist nontrivial global solutions. When p - m +2/ N , the examples we constructed suggest that for some p ( x ) all nontrivial solutions blow up and for others there exist global solutions. The situation is totally different in bounded domains. There is only one critical exponent p = m , while there are three factors, p ( x ); m and properties of the domain, interacting with each other. If p + > m , there are blow-up solutions as in R N . If p + m , all solutions exist globally in time. If p ( x )> m or the domain is small enough, there are global solutions. The most interesting part is that for some p ( x ) satisfying p - m p + , we find the Fujita phenomenon in the bounded domain.

Published
2016

6. Existence and uniqueness of weak solutions for a non-uniformly parabolic equation

Author

Cai, Yongyong and Zhou, Shulin

Subjects
*EXISTENCE theorems, *NUMERICAL solutions to parabolic differential equations, *BOUNDARY value problems, *MATHEMATICAL proofs, *MATHEMATICAL analysis, *MATHEMATICAL physics
Abstract

Abstract: In this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial–boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the special cases of this equation. [Copyright &y& Elsevier]

Published
2009
Full Text
View/download PDF

8. Existence and uniqueness of weak solutions for a generalized thin film equation

Author

Xu, Meng and Zhou, Shulin

Subjects
*THIN films, *SOLID state electronics, *DIFFERENTIAL equations, *COMPLEX variables
Abstract

Abstract: In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a generalized thin film equation. In addition, we present some interesting results on the regularity of weak solutions. [Copyright &y& Elsevier]

Published
2005
Full Text
View/download PDF

9. Existence and uniqueness of weak solutions for a 2D low-curvature equation.

Author

Wang, Lihe, Zhang, Chao, and Zhou, Shulin

Subjects
*CURVATURE measurements, *EXISTENCE theorems, *UNIQUENESS (Mathematics), *TWO-dimensional models, *BOUNDARY value problems, *IMAGE analysis
Abstract

In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a two-dimensional low-curvature equation, which is related to image analysis. [ABSTRACT FROM AUTHOR]

Published
2017
Full Text
View/download PDF

10. Entropy and renormalized solutions to the general nonlinear elliptic equations in Musielak–Orlicz spaces.

Author

Li, Ying, Yao, Fengping, and Zhou, Shulin

Subjects
*ELLIPTIC equations, *NONLINEAR equations, *ENTROPY (Information theory)
Abstract

In this paper we mainly prove the existence and uniqueness of entropy solutions and the uniqueness of renormalized solutions to the general nonlinear elliptic equations in Musielak-Orlicz spaces. Moreover, we also obtain the equivalence of entropy solutions and renormalized solutions in the present conditions. [ABSTRACT FROM AUTHOR]

Published
2021
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results