theory of analytic semigroups, Fixed point arguments, Inverse problems for integral equations, fixed point arguments, Combustion of a material with memory, inverse problems, Identification problem, Applied Mathematics, Singular nonlinear integral equations, Abstract integral equations, integral equations in abstract spaces, quasilinear integrodifferential system in non-normal form, optimal regularity results, Quasilinear integrodifferential system in non-normal form, phase-field model with memory, combustion of a material with memory, Phase-field model with memory, Integro-ordinary differential equations, Optimal regularity results, Systems of nonlinear integral equations, identification problem, Analysis, Theory of analytic semigroups