A mathematical model for the use of energy resources: a singular parabolic equation

    Daniel López-García Affiliation
    ; Rosa Pardo Affiliation


We consider a singular parabolic equation, for , arising in symmetric boundary layer flows. Here is a bounded domain with C2 boundary is bounded, and T > 0 is some fixed time. We establish sufficient conditions for the existence and uniqueness of a weak solution of this singular parabolic equation with Dirichlet boundary conditions, and we investigate its regularity.

There are two different cases depending on β. If β < 1, for any initial data, there exists a unique weak solution, which in fact is a strong solution. The singularity is removable when β < 1. While if β = 1, there exists a unique solution of the singular parabolic problem  The initial data cannot be arbitrarily chosen. In fact, if f is continuous and , as t → 0, then, this solution converges, as t → 0, to the solution of the elliptic problem, for , with Dirichlet boundary conditions. Hence, no initial data can be prescribed when β = 1, and the singularity in that case is strong.

Keyword : singular parabolic equation, degenerate parabolic equations, existence, uniqueness, symmetric boundary layer, regularity

How to Cite
López-García, D., & Pardo, R. (2020). A mathematical model for the use of energy resources: a singular parabolic equation. Mathematical Modelling and Analysis, 25(1), 88-109.
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Jan 13, 2020
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