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MiS Preprint
69/1998
Existence and uniqueness of energy weak solutions to boundary and obstacle problems for quasilinear elliptic-parabolic equations
Alexander V. Ivanov and Jose Francisco Rodrigues
Abstract
We prove existence and uniqueness of weak solutions to initial-boundary value problem and problem with inner obstacle for elliptic-parabolic equations $$\partial_i b(u)-div\{|\delta(u)|^{m-2} \delta (u)\} =f(x,t)$$,$$\delta (u) = \nabla u + k(b(u)) \overrightarrow{\rm e},\ \ \ |\overrightarrow{\rm e}| = 1, m> 1$$ with a monotone nondecreasing function b. These equations arise in the theory of non-Newtonian filtation and mathematical glaciology.
