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Existence and uniqueness of similarity solutions of a generalized heat equation arising in a model of cell migration

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  • We study similarity solutions of a nonlinear partial differential equation that is a generalization of the heat equation. Substitution of the similarity ansatz reduces the partial differential equation to a nonlinear second-order ordinary differential equation on the half-line with Neumann boundary conditions at both boundaries. The existence and uniqueness of solutions is proven using Ważewski's Principle.
    Mathematics Subject Classification: Primary: 35C06, 34B40, 34B15; Secondary: 35Q92.


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