scholarly journals Initiation of thermal explosion by intense light: criticality dependence on data and parameters

1987 ◽  
Vol 28 (3) ◽  
pp. 287-295 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Steady State Solution ◽  
Linear Ordinary Differential Equation ◽  
Critical Parameters ◽  
Linear Parabolic Equation ◽  
Thermal Ignition ◽  
Non Linear ◽  
Intense Light

AbstractA model for thermal ignition by intense light is studied. The governing non-linear parabolic equation is linearized in a two-step manner with the aid of a non-linear ordinary differential equation which captures the salient features of the non-linear parabolic equation. The critical parameters are computed from the steady-state solution of the ordinary differential equation, which can be obtained without actually solving the equation. Comparison with available data shows that the present method yields good results.

scholarly journals Classroom Note: Numerical solutions of Nagumo's equation

1999 ◽  
Vol 3 (2) ◽  
pp. 189-193 ◽  
Author(s):  
M. Iqbal
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solutions ◽  
Linear Ordinary Differential Equation ◽  
Bounded Solutions ◽  
Third Order ◽  
Non Linear

Nagumo's equation is a third order non-linear ordinary differential equation d3udx3−cd2udx2+f′(u)dudx−(b/c)u=0 where f(u)=u(1−u)(u−α) , 0<α<1 . In this paper we have developed a technique to determine those values of the parameters a,b and c which permit non-constant bounded solutions.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

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