Continuous dependence result for the higher-order conduction within the second gradient of type III

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Abstract

This study investigated the spatial behavior and structural stability of solutions for a higher-order heat conduction model within the second gradient theory of type III. By constructing a tailored energy functional and employing integral-differential inequality techniques, we derived a continuous dependence estimate for the solution with respect to the elastic coefficient µ. Our results demonstrate that the energy not only decays exponentially with respect to the spatial variable z, but also diminishes as the parameter µ tends to zero. This work extends the understanding of structural stability in unbounded domains and underscores the robustness of the model under perturbations of material parameters.

Keywords

integral-differential inequality / structural stability / sontinuous dependence / second gradient of type III

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