Solution of the problem of stress concentration around holes in thin shells of zero gaussian curvature by reducing the solving equation to an ordinary differential equation in terms of a complex variable

1989 ◽  
Vol 21 (11) ◽  
pp. 1583-1589 ◽  
Author(s):  
Yu. V. Goloveshkin
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Stress Concentration ◽  
Complex Variable ◽  
Gaussian Curvature ◽  
Thin Shells ◽  
Zero Gaussian Curvature

Stiff ordinary differential equation test problems

1973 ◽  
Vol 8 (4) ◽  
pp. 10-12
Author(s):  
A. R. Curtis
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Test Problems

scholarly journals Classification of extinction profiles for a one-dimensional diffusive Hamilton–Jacobi equation with critical absorption

2018 ◽  
Vol 148 (3) ◽  
pp. 559-574
Author(s):  
Razvan Gabriel Iagar ◽  
Philippe Laurençot
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Jacobi Equation ◽  
Threshold Value ◽  
Monotonicity Property ◽  
Fast Diffusion ◽  
Extinction Time ◽  
One Step ◽  
Hamilton Jacobi Equation

A classification of the behaviour of the solutions f(·, a) to the ordinary differential equation (|f′|p-2f′)′ + f - |f′|p-1 = 0 in (0,∞) with initial condition f(0, a) = a and f′(0, a) = 0 is provided, according to the value of the parameter a > 0 when the exponent p takes values in (1, 2). There is a threshold value a* that separates different behaviours of f(·, a): if a > a*, then f(·, a) vanishes at least once in (0,∞) and takes negative values, while f(·, a) is positive in (0,∞) and decays algebraically to zero as r→∞ if a ∊ (0, a*). At the threshold value, f(·, a*) is also positive in (0,∞) but decays exponentially fast to zero as r→∞. The proof of these results relies on a transformation to a first-order ordinary differential equation and a monotonicity property with respect to a > 0. This classification is one step in the description of the dynamics near the extinction time of a diffusive Hamilton–Jacobi equation with critical gradient absorption and fast diffusion.

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