An elliptic-parabolic problem with a nonlocal boundary condition
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The authors derive a nonlinear elliptic-parabolic problem describing the one-dimensional flow of a liquid in an unsaturated porous medium. The originality of the model appears in a nonlocal boundary condition on the unknown, which is chosen to be the difference between the pressure of the liquid and the pressure of the gas filling the medium. The existence of a unique local weak solution is then shown. The behaviour of the free interface is also investigated when the time tends to the upper bound of the interval on which the authors have defined the weak solution.
- University of Technology Russian Federation
- Technical University Eindhoven Netherlands
unique local weak solution, elliptic-parabolic problem, flow of a liquid, free interface, Flows in porous media; filtration; seepage, existence, Existence of generalized solutions of PDE, porous medium, Degenerate parabolic equations, Local existence and uniqueness theorems (PDE), nonlocal boundary condition
unique local weak solution, elliptic-parabolic problem, flow of a liquid, free interface, Flows in porous media; filtration; seepage, existence, Existence of generalized solutions of PDE, porous medium, Degenerate parabolic equations, Local existence and uniqueness theorems (PDE), nonlocal boundary condition
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