Global Solutions and Quenching to a Class of Quasilinear Parabolic Equations
نویسنده
چکیده
In this paper we consider a quasilinear parabolic equation a(ux)ut = uxx (a(s) a0 > 0) subject to appropriate initial and boundary conditions. This equation can be used to describe the uni-directional motion of uid in soft tissue. A criterion is found to ensure the global solvability or nite time quenching (i.e. ux becomes unbounded in nite time). A concrete example is that for a(s) = (1 + s), the problem has a global solution if p 2 while the nite time quenching occurs if p > 2. The pro le near the quenching time such as the single point quenching and the quenching rate are also studied. Partial results are generalized into several space dimensions. This work is partially supported by US National Science Foundation Grant DMS 90-24986 and NSERC of Canada.
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