Article
Mathematics, Applied
Yuzhu Yang, Zhongping Li
Summary: This paper discusses the behavior of a quasilinear parabolic-elliptic chemotaxis system with a space dependent logistic source in a ball domain, proving the existence of solutions that blow up in finite time.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Yuya Tanaka
Summary: This paper deals with the quasilinear parabolic-elliptic chemotaxis system with logistic source and nonlinear production. Boundedness and finite-time blow-up conditions for solutions are provided under certain parameters.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Yutaro Chiyo, Tomomi Yokota
Summary: This paper investigates the dynamical behavior of the quasilinear attraction-repulsion chemotaxis system in a bounded domain. The results include global existence, boundedness and blow-up. The study classifies the system behavior under different parameter conditions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Yuya Tanaka
Summary: This paper discusses the conditions for solutions of the Keller-Segel system with a logistic source to blow up in finite time. Previous studies have established blow-up conditions under different parameter values, providing a theoretical basis for further research.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Yuya Tanaka, Tomomi Yokota
Summary: This paper deals with the finite-time blow-up of solutions to the quasilinear degenerate parabolic-elliptic chemotaxis system. The purpose of this paper is to establish the finite-time blow-up for the above degenerate chemotaxis system within a concept of weak solutions with a moment inequality leading to blow-up.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics, Applied
Mi Jin Lee, Jum-Ran Kang
Summary: This study focuses on the blow-up result of a quasilinear von Karman equation of memory type with acoustic boundary conditions. The authors prove the finite-time blow-up result of the solution under suitable conditions on the initial data. The asymptotic behavior of the solution to the von Karman equation has also been considered by many researchers.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Juntang Ding, Chenyu Dong
Summary: This paper investigates the blow-up problem of a weakly coupled quasilinear parabolic system and provides a sufficient condition to ensure that the positive solution of the problem must be a blow-up solution with a finite blow-up time. Additionally, upper bounds on the blow-up time and an upper estimate of the blow-up rate on the solution are obtained.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics
Tian Xiang
Summary: This work mainly focuses on the study of nonnegative classical solutions to a Neumann initial-boundary value problem for a parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system. The results obtained provide important insights into the phenomenon of pure haptotaxis and mass blow-up in the presence of temporal nonlocality brought by haptotaxis.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Michael Winkler
Summary: The paragraph introduces a mathematical model of a chemotaxis system and provides an existence result for the solution when certain conditions are met.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
Article
Mathematics
Ala A. Talahmeh, Salim A. Messaoudi, Mohamed Alahyane
Summary: This paper explores a nonlinear viscoelastic wave equation with variable exponents and proves a finite-time blow-up result under specific conditions. Numerical applications are also provided to illustrate the theoretical findings.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Mathematics, Applied
Hu Chen, Martin Stynes
Summary: Time-fractional initial-boundary value problems are studied, showing that the solution converges to the solution of the classical parabolic initial-boundary value problem as alpha approaches 1(-). Rigorous analyses of numerical methods for this problem typically have error bounds that blow up as alpha -> 1(-), but in some cases, these analyses can be modified to obtain robust error bounds.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2021)
Article
Mathematical & Computational Biology
Ruxi Cao, Zhongping Li
Summary: This paper discusses a quasilinear parabolic-elliptic-elliptic attraction-repulsion system. It proves that solutions with initial mass concentrating enough in a small ball centered at origin will blow up in finite time, under certain conditions. However, the system admits a global bounded classical solution for suitable smooth initial datum.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Applied
Qunfei Long
Summary: In this paper, we improve a method for establishing finite time blow-up solutions on parabolic or pseudoparabolic equations and apply it to study the finite time blow-up and upper bound for the blow-up time on the initial boundary value problem. We prove that a sufficient condition for the existence of finite time blow-up solutions is I(u0)<0, and introduce a new upper bound 2(p-1)-1||u0||H012(p-1)|| backward difference u0||22-2(p+1)J(u0) for the blow-up time, which generalizes previous results. Additionally, we estimate the upper blow-up rate of these solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Yuusuke Sugiyama
Summary: This paper considers the blowup of solutions to the parameterized nonlinear wave equation. Previous research reported the existence of finite time blowup solutions for lambda = 1 and 2. The paper extends the blowup result with lambda = 1 to the case where lambda belongs to (0, 1] by introducing a new L2/lambda estimate, and discusses properties of the blowup solution.
INDIANA UNIVERSITY MATHEMATICS JOURNAL
(2022)
Article
Mathematics, Applied
Yulan Wang, Michael Winkler
Summary: The paper investigates a chemotaxis system in a ball-shaped Omega subset of R-n, where an explosive solution is found for the corresponding initial-boundary value problem under certain conditions on the coefficient D.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2023)
