JP Journal of Heat and Mass Transfer
Volume 15, Issue 3, Pages 569 - 578
(August 2018) http://dx.doi.org/10.17654/HM015030569 |
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EXISTENCE AND UNIQUENESS OF SOLVING BOUNDARY PROBLEM FOR QUASI-LINEAR PARABOLIC EQUATION WITH INTEGRAL CONDITION ON FREE BOUNDARY
P. Martyniuk, O. Ostapchuk, T. Tsvietkova and O. Michuta
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Abstract: Qualitative studies are carried out of quasi-linear parabolic equation in the domain with free mobile boundary. The movement of a boundary is described by integral cinematic boundary condition. The existence and uniqueness is proved of the local in time solution of corresponding one-dimensional boundary problem in Holder spaces. The researched boundary problem is a mathematical model of the consolidation of saturated porous media. |
Keywords and phrases: quasi-linear parabolic equations, free boundary, existence and uniqueness of solution. |
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