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
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.
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The author has been supported by the Studienstiftung des deutschen Volkes
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Schätzler, L. Existence for singular doubly nonlinear systems of porous medium type with time dependent boundary values. J Elliptic Parabol Equ 5, 383–421 (2019). https://doi.org/10.1007/s41808-019-00048-7
- Porous medium equation
- Doubly nonlinear systems
- Minimizing movements
Mathematics Subject Classification