global unique solvability
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Author(s):  
Novrianti Novrianti ◽  
Okihiro Sawada ◽  
Naoki Tsuge

The time-global unique solvability on the reaction–diffusion equations for preypredator models and dormancy on predators is established. The crucial step is to construct time-local nonnegative classical solutions by using a new approximation associated with time-evolution operators. Although the system does not equip usual comparison principles, a priori bounds are derived, so solutions are extended time-globally. Via observations to the corresponding ordinary differential equations, invariant regions and asymptotic behaviors of solutions are also investigated.


2020 ◽  
Vol 269 (2) ◽  
pp. 1319-1348 ◽  
Author(s):  
P. Braz e Silva ◽  
F.W. Cruz ◽  
M. Loayza ◽  
M.A. Rojas-Medar

2020 ◽  
Vol 28 (1) ◽  
pp. 43-52
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
Zhanna Dmitrievna Totieva

AbstractThe integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained.


2013 ◽  
Vol 43 (1) ◽  
pp. 73-93 ◽  
Author(s):  
Lennart Jansen ◽  
Michael Matthes ◽  
Caren Tischendorf

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