On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium |
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| Institution: | Facultad de Matematicas, Universidad Complutense de Madrid, 28040 Madrid, Spain;Computer and Automation Institute of the Hungarian Academy of Science, Budapest, Hungary |
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| Abstract: | We prove the uniqueness (as well as the existence and regularity) of solutions of the Cauchy problem and of the first and mixed boundary value problems for the equation ut = φ(u)xx + b(u)x. (E) φ and b are assumed to belong to a large class of functions, including, in particular, cases φ(u) = um, b(u) = uλ, m ⩾ 1 and λ > 0. |
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