Journal of Elliptic and Parabolic Equations

, Volume 5, Issue 2, pp 383–421 | Cite as

Existence for singular doubly nonlinear systems of porous medium type with time dependent boundary values

  • Leah SchätzlerEmail author


In this paper we prove the existence of variational solutions to the Cauchy–Dirichlet problem with time dependent boundary values associated with doubly nonlinear systems
$$\begin{aligned} \partial _t \big (|u|^{m-1}u\big ) - {{\,\mathrm{div}\,}}(D_\xi f(Du)) = 0 \end{aligned}$$
with \(m>1\) and a convex function f satisfying a standard p-growth condition for an exponent \(p \in (1,\infty )\). The proof relies on a nonlinear version of the method of minimizing movements.


Porous medium equation Doubly nonlinear systems Existence Minimizing movements 

Mathematics Subject Classification

35K86 49J40 49J45 



The author has been supported by the Studienstiftung des deutschen Volkes

Compliance with ethical standards

Conflict of interest

Following the requirements of the journal, the author declares that she has no conflict of interest

Human/animal rights statement

Adding to the beauty of mathematics, this article does not contain any studies with human participants or animals.


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Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany

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