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Aims: We investigate from a theoretical perspective if space asteroseismologycan be used to distinguish between different thermal structures and shapes ofthe near-core mixing profiles for different types of coherent oscillation modesin massive stars with convective cores, and if this capacity depends on theevolutionary stage of the models along the main sequence. Methods: We compute1D stellar structure and evolution models for four different prescriptions ofthe mixing and temperature gradient in the near-core region. Their effect onthe frequencies of dipole prograde gravity modes in both Slowly Pulsating B and$\beta$ Cep stars is investigated, as well as for pressure modes in $\beta$ Cepstars. Results: A comparison between the mode frequencies of the differentmodels at various stages during the main sequence evolution reveals that theyare more sensitive to a change in temperature gradient than to the exact shapeof the mixing profile in the near-core region. Depending on the duration of theobserved light curve, one can distinguish between either just the temperaturegradient, or also between the shapes of the mixing coefficient. The relativefrequency differences are in general larger for more evolved models, and arelargest for the higher-frequency pressure modes in $\beta$ Cep stars.Conclusions:In order to unravel the core boundary mixing and thermal structureof the near-core region, one must have asteroseismic masses and radii with$\sim 1\%$ relative precision for hundreds of stars.

Probing the shape of the mixing profile and of the thermal structure at the convective core boundary through asteroseismology