We consider an initial-boundary-value problem for a semilinear parabolic equation with nonlinear nonlocal boundary conditions. We prove the principle of comparison, establish the existence of local solutions, and study the problem of uniqueness and nonuniqueness.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 2, pp. 162–174, February, 2016.
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Gladkov, A.L., Kavitova, T.V. Initial-Boundary-Value Problem for a Semilinear Parabolic Equation with Nonlinear Nonlocal Boundary Conditions. Ukr Math J 68, 179–192 (2016). https://doi.org/10.1007/s11253-016-1217-2
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DOI: https://doi.org/10.1007/s11253-016-1217-2