Global stability result for parabolic Cauchy problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mourad Choulli ◽  
Masahiro Yamamoto
Keyword(s):  
New York ◽  
Partial Differential Equations ◽  
Global Stability ◽  
Classical Problem ◽  
Stability Result ◽  
Cauchy Problems ◽  
Smooth Solutions ◽  
Linear Partial Differential Equations ◽  
Ill Posed ◽  
The Stability

AbstractUniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover, New York, 1953], these kind of problems are known to be ill-posed and even severely ill-posed. Until now, there are only few partial results concerning the quantification of the stability of parabolic Cauchy problems. We bring in the present work an answer to this issue for smooth solutions under the minimal condition that the domain is Lipschitz.

scholarly journals Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1164
Author(s):  
Weiwei Ling ◽  
Pinxia Wu ◽  
Xiumei Li ◽  
Liangjin Xie
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Control Strategy ◽  
Theoretical Basis ◽  
Dynamic Properties ◽  
Transmission Mechanism ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Vector Borne ◽  
Citrus Trees

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different I0 in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of I0, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure.

scholarly journals Qualitative properties of mathematical model of English language education

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Atena Ghasemabadi ◽  
Nahid Soltanian
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Equilibrium Point ◽  
English Language ◽  
Language Education ◽  
Qualitative Properties ◽  
English Language Education ◽  
Compound Matrices ◽  
Reproduction Numbers ◽  
Coexistence Equilibrium

AbstractThis paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

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