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Journal of Applied Mechanics and Technical Physics

2013 year, number 2

Existence and Uniqueness of the Solution of the Boundary-Value Problem for a Parabolic Equation of Unsteady Filtration

A. L. Kazakov, A. A. Lempert
Keywords: nonlinear filtration, partial differential equations, boundary-value problem, existence and uniqueness theorem, series, convergence
Pages: 251-258


The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.