A nonlinear oblique derivative boundary value problem for the heat equation: Analogy with the porous medium equation
نویسندگان
چکیده
The problem under investigation is the heat equation in the upper half-plane, to which the di usion in the longitudinal direction has been suppressed, and augmented with a nonlinear oblique derivative condition. This paper proves global existence and qualitative properties to the Cauchy Problem for this model, furthering the study [18] of the self-similar solutions. The qualitative behaviour of the solutions exhibits a strong analogy with the porous medium equation: propagation with compact support and nite speed, free boundary relation and time-asymptotic convergence to self-similar solutions.
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