Volterra equations which model explosion in a diffusive medium

DOI10.1216/jiea/1181075776zbMath0804.45002OpenAlexW2058604696MaRDI QIDQ1325743

Catherine A. Roberts, D. Glenn Lasseigne, W. Edward Olmstead

Publication date: 12 July 1994

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jiea/1181075776

zbMATH Keywords

shear band formationnonlinear Volterra integral equationssolid combustionexplosion modelling

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Combustion (80A25)

Related Items (30)

Stability, instability, and blowup for time fractional and other nonlocal in time semilinear subdiffusion equations ⋮ Coupled Volterra equations with blow-up solutions ⋮ Fractional collocation boundary value methods for the second kind Volterra equations with weakly singular kernels ⋮ Conditions for blow-up of solutions of some nonlinear Volterra integral equations ⋮ Uniqueness of solutions to an Abel type nonlinear integral equation on the half line ⋮ Blow-up solutions of nonlinear Volterra integro-differential equations ⋮ The series expansions and blow-up time estimation for the solutions of convolution Volterra-Hammerstein integral equations ⋮ Blow-up behavior of Hammerstein-type Volterra integral equations ⋮ A note on blow-up solutions to some nonlinear Volterra integral equations ⋮ Numerical and asymptotic analysis of a localized heat source undergoing periodic motion ⋮ Remarks on coupled Abel type integral equations ⋮ Critical speed to avoid blow-up in diffusive medium ⋮ Characterizing the blow-up solutions for nonlinear volterra integral equations ⋮ Smoothing transformation for numerical solution of nonlinear weakly singular Volterra integral equations using quasilinearization and product integration methods ⋮ Analysis of blow-up behavior of solutions to CVIEs ⋮ On the contributions of W. Edward Olmstead ⋮ Coupled Volterra integral equations with blowing up solutions ⋮ Blow-up conditions for nonlinear Volterra integral equations with power nonlinearity ⋮ Continuous and discrete one dimensional autonomous fractional ODEs ⋮ BLOW-UP SOLUTIONS OF THE TWO-DIMENSIONAL HEAT EQUATION DUE TO A LOCALIZED MOVING SOURCE ⋮ Blow-up solutions to a system of nonlinear Volterra equations ⋮ A nonlinear Abel equation on the whole line ⋮ Blow-up time for solutions to some nonlinear Volterra integral equations ⋮ The existence problem for a nonlinear Abel equation on the half-line ⋮ A new upper estimation for the blow-up time of solutions of a Volterra integral equation and its application to the modeling of the formation of shear bands ⋮ A multiple nonlinear Abel type integral equation ⋮ Blowing up behavior for a class of nonlinear VIEs connected with parabolic PDEs ⋮ Thermal blow-up in a finite strip with superdiffusive properties ⋮ Blowup in diffusion equations: A survey ⋮ Analysis of explosion for nonlinear Volterra equations

Cites Work

• Unnamed Item
• Ignition of a combustible solid by convection heating
• Evolution of deflagration in a cold combustible subjected to a uniform energy flux
• Ignition of a Combustible Half Space
• Ignition or nonignition of a combustible solid with marginal heating
• The Role of Critical Exponents in Blowup Theorems
• Asymptotic Solution to a Class of Nonlinear Volterra Integral Equations. II
• Asymptotic Solution to a Class of Nonlinear Volterra Integral Equations

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