Quarterly of Applied Mathematics · 1996 · 45 citations · 6 references
Natural SciencesMathematicsPhysicsCombustionDifferential EquationsFluid DynamicsIntegral EquationsNonlinear DynamicsAsymptotic ExpansionsBlow-up PhenomenaGrowth RatesNonlinear Integral EquationsShear Band FormationVolterra EquationsVolterra Integral EquationsVolterra Theory
An investigation is made of the blow-up growth property of the solution to certain nonlinear Volterra integral equations which model explosive behavior in a diffusive medium. The basic results provide the asymptotic form of the blow-up solution for a large class of kernels as well as various nonlinearities based on examples from solid combustion and adiabatic shear band formation.
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Ignition of a Combustible Half Space
W. E. Olmstead · SIAM Journal on Applied Mathematics · 1983 · 35 citations