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In this paper, we study a nonlocal degenerate parabolic equation of order{\alpha} + 2 for 0<{\alpha}<2. The equation is a generalization of the onearising in the modeling of hydraulic fractures studied by Imbert and Mellet in2011. Using the same approach, we prove the existence of solutions for thisequation for 0<{\alpha}<2 and for nonnegative initial data satisfyingappropriate assumptions. The main difference is the compactness results due todifferent Sobolev embeddings. Furthermore, for {\alpha} > 1, we construct anonnegative solution for nonnegative initial data under weaker assumptions.

Study of a family of higher order nonlocal degenerate parabolic equations: from the porous medium equation to the thin film equation