MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Existence and uniqueness of energy weak solutions to boundary and obstacle problems for quasilinear elliptic-parabolic equations

Alexander V. Ivanov and Jose Francisco Rodrigues


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.


Related publications

2000 Repository Open Access
Alexander V. Ivanov and Jose Francisco Rodrigues

Existence and uniqueness of a weak solution to the initial mixed boundary value problem for quasilinear elliptic-parabolic equations

In: Journal of mathematical sciences, 109 (2000) 5, pp. 1851-1866