scholarly journals A second-order conservational difference scheme for the one-dimensional model of martensitic transformations with nonlinear boundary conditions

2011 ◽  
Vol 35 (7) ◽  
pp. 3484-3494
Author(s):  
Li-ping He ◽  
J.H. Zhang
Keyword(s):  
Boundary Conditions ◽  
Difference Scheme ◽  
Nonlinear Boundary ◽  
Martensitic Transformations ◽  
Nonlinear Boundary Conditions ◽  
Second Order ◽  
Dimensional Model ◽  
One Dimensional ◽  
The One

scholarly journals Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions

2019 ◽  
Vol 39 (5) ◽  
pp. 675-689
Author(s):  
D. D. Hai ◽  
X. Wang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Positive Parameter ◽  
One Dimensional ◽  
Existence Of Positive Solutions ◽  
The One

We prove the existence of positive solutions for the \(p\)-Laplacian problem \[\begin{cases}-(r(t)\phi (u^{\prime }))^{\prime }=\lambda g(t)f(u),& t\in (0,1),\\au(0)-H_{1}(u^{\prime }(0))=0,\\cu(1)+H_{2}(u^{\prime}(1))=0,\end{cases}\] where \(\phi (s)=|s|^{p-2}s\), \(p\gt 1\), \(H_{i}:\mathbb{R}\rightarrow\mathbb{R}\) can be nonlinear, \(i=1,2\), \(f:(0,\infty )\rightarrow \mathbb{R}\) is \(p\)-superlinear or \(p\)-sublinear at \(\infty\) and is allowed be singular \((\pm\infty)\) at \(0\), and \(\lambda\) is a positive parameter.

The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

2021 ◽  
Vol 88 (1-2) ◽  
pp. 155
Author(s):  
Halima Nachid ◽  
F. N'Gohisse ◽  
N'Guessan Koffi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lower And Upper Bounds ◽  
Linear Reaction ◽  
The One ◽  
Quenching Time

We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

Nonlinear boundary conditions for nonlinear second order differential operators on C[0,1]

2001 ◽  
Vol 76 (5) ◽  
pp. 391-400 ◽  
Author(s):  
A. Favini ◽  
G. R. Goldstein ◽  
J. A. Goldstein ◽  
S. Romanelli
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Differential Operators ◽  
Nonlinear Boundary Conditions ◽  
Second Order
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