Analytic-numerical solutions of diffusion mathematical models with delays
Computers & Mathematics with Applications
Dual-phase lag effects on thermal damage to biological tissues caused by laser irradiation
Computers in Biology and Medicine
Analytic solution of mixed problems for thegeneralized diffusion equation with delay
Mathematical and Computer Modelling: An International Journal
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Lagging models of heat conduction, such as the Dual-Phase-Lag or the Single-Phase-Lag models, lead to heat conduction equations in the form of partial differential equations with delays or to partial differential equations of hyperbolic type, and have been considered to model microscale heat transfer in engineering problems or bio-heat transfer in medical treatments. In this work we obtain explicit solutions for bidimensional lagging models of heat conduction, with different types of boundary conditions, in the form of infinite series solutions, allowing the construction of analytic-numerical solutions with bounded errors. Numerical examples, showing differences between models and the influence of parameters, are discussed.