Abstract
A one-dimensional Keller-Segel system which is defined through uniformly elliptic operators having variable coefficients is considered. In the main theorems, the local existence and uniqueness of the mild solution of the system are proved. The main method to construct the mild solution is an argument of successive approximations by means of strongly continuous semi-groups.
Communicated by Giuseppe Di Fazio
Acknowledgement
The author expresses her deep gratitude to Prof. Sergio Albeverio who gives her insightful comments and suggestions on this paper. Prof. Kiyomasa Narita is also deely acknowledged for the beneficent discussions from the point of view of probabilistic theory. She has to express her deep thanks to Prof. Noriaki Yamazaki for his accurate advice on the present research. The author would like to offer her thanks to Prof. Atsushi Yagi and Prof. Koichi Osaki who notice her the existence of the important papers [1] and [17]. She also expresses her sincere thanks to Prof. Michael Winkler for giving her his benefit papers. Prof. Minoru W. Yoshida, who discusses with the author on the fundamental structure of the present problem, is acknowledged. Finally she should acknowledge the constructive comments of the referee, which led to the substantial improvements of the paper.
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© 2018 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- A multi-parameter generalization of the symmetric algorithm
- Single identities forcing lattices to be Boolean
- Weighted uniform density ideals
- A generalized class of restricted Stirling and Lah numbers
- The Riemann hypothesis and universality of the Riemann zeta-function
- Distance functions on the sets of ordinary elliptic curves in short Weierstrass form over finite fields of characteristic three
- The drazin inverse of the sum of two matrices
- Refinements of the majorization-type inequalities via green and fink identities and related results
- Characterizations and properties of graphs of Baire functions
- Some improvements of the young mean inequality and its reverse
- On characteristic of bounded analytic functions involving hyperbolic derivative
- A uniqueness problem for entire functions related to Brück’s conjecture
- System of nonlocal resonant boundary value problems involving p-Laplacian
- Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
- Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces
- Characterization of rough weighted statistical limit set
- Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
- On generalized 4-th root metrics of isotropic scalar curvature
- Compactifications from generators and relations
- Diophantine quadruples with values in k-generalized Fibonacci numbers