Abstract
We consider the boundary-value problem in a semibounded interval for a fourth-order equation with “double degeneracy”: the small parameter in the equation multiplies the product of the unknown function vanishing on the boundary and its highest derivative. Such a problem arises in the description of the motion of weak solutions of polymers near a critical point. For the zero value of the parameter, the solution is the classical Hiemenz solution. We prove the unique solvability of the problem for nonnegative values of the parameter not exceeding 1.
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Acknowledgments
The author wishes to express deep gratitude to V. V. Pukhnachev for attracting the author’s attention to this research area and valuable advice.
Funding
This work was supported by the Russian Foundation for Basic Research under grant 16-01 -00127.
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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 5, pp. 723-735.
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Petrova, A.G. On the Unique Solvability of the Problem of the Flow of an Aqueous Solution of Polymers near a Critical Point. Math Notes 106, 784–793 (2019). https://doi.org/10.1134/S0001434619110117
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DOI: https://doi.org/10.1134/S0001434619110117