Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data

2019 ◽  
Vol 266 (11) ◽  
pp. 7525-7544 ◽  
Author(s):  
Dietmar Hömberg ◽  
Shuai Lu ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problem ◽  
Parabolic System ◽  
Nonlinear Parabolic System ◽  
Integral Term ◽  
Dirichlet Data ◽  
Nonlinear Parabolic

Identification of two coefficients with data of one component for a nonlinear parabolic system

2012 ◽  
Vol 91 (11) ◽  
pp. 2073-2081 ◽  
Author(s):  
Michel Cristofol ◽  
Patricia Gaitan ◽  
Hichem Ramoul ◽  
Masahiro Yamamoto
Keyword(s):  
Parabolic System ◽  
Nonlinear Parabolic System ◽  
Nonlinear Parabolic

scholarly journals EXISTENCE, UNIQUENESS AND APPROXIMATION OF A DOUBLY-DEGENERATE NONLINEAR PARABOLIC SYSTEM MODELLING BACTERIAL EVOLUTION

2007 ◽  
Vol 17 (07) ◽  
pp. 1095-1127 ◽  
Author(s):  
JOHN W. BARRETT ◽  
KLAUS DECKELNICK
Keyword(s):  
Parabolic System ◽  
Existence And Uniqueness ◽  
Finite Element Approximation ◽  
System Modelling ◽  
Element Approximation ◽  
Nonlinear Parabolic System ◽  
Spatiotemporal Evolution ◽  
Nonlinear Parabolic ◽  
Flux Boundary Conditions ◽  
Bacterium Species

We consider the following nonlinear parabolic system [Formula: see text] subject to no flux boundary conditions, and non-negative initial data u0 and v0 on u and v. Here we assume that c > 0, θ ≥ 0 and that [Formula: see text] is increasing with f(0) = 0. The system is possibly doubly-degenerate in that [Formula: see text] is only non-negative, and ψ ∈ C1([0,∞)) ∩ C2((0,∞)) is convex, strictly increasing with ψ(0) = 0 and possibly ψ'(0) = 0. The above models the spatiotemporal evolution of a bacterium species on a thin film of nutrient, where u is the nutrient concentration and v is the bacterial cell density. Under some further mild technical assumptions on b and ψ, we prove the existence and uniqueness of a weak solution to the above system. Moreover, we prove error bounds for a fully practical finite element approximation of this system. All of our results apply to the choices b(r) ≔ rq and ψ(r) ≔ rp with q ≥ 2 and p ≥ 1, for example.

scholarly journals On a nonlinear parabolic system-modeling chemical reactions in rivers

2005 ◽  
Vol 4 (4) ◽  
pp. 889-899 ◽  
Author(s):  
Wenxiong Chen ◽  
◽  
Congming Li ◽  
Eric S. Wright ◽  
◽  
...  
Keyword(s):  
Chemical Reactions ◽  
Parabolic System ◽  
System Modeling ◽  
Nonlinear Parabolic System ◽  
Nonlinear Parabolic
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