Evolutionary Problems in Non-Cylindrical Domains

Bögelein V, Duzaar F, Scheven C (2021)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2021

Publisher: Springer-Verlag Italia s.r.l.

Edited Volumes: Springer INdAM Series

Series: Springer INdAM Series

Book Volume: 46

Pages Range: 43-60

DOI: 10.1007/978-3-030-73778-8_3

Abstract

This survey article presents an existence theory developed in Bögelein et al. (SIAM J Math Anal 50(3): 3007–3057, 2018) for vector-valued gradient flows of integral functionals in bounded non-cylindrical domains E⊂ ℝn× [ 0, T). The associated system of differential equations takes the form ∂tu−divDξf(x,u,Du)=−Duf(x,u,Du)inE, $$\displaystyle \begin{aligned} \partial _t u - \operatorname {\mathrm {div}} D_\xi f(x,u,Du) = -D_u f(x,u,Du) \qquad \mbox{in }E, \end{aligned} $$ for an integrand f(x, u, Du) that is convex and coercive with respect to the W1, p-norm for p > 1.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Universität Duisburg-Essen (UDE) DE Germany (DE) Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT)

How to cite

APA:

Bögelein, V., Duzaar, F., & Scheven, C. (2021). Evolutionary Problems in Non-Cylindrical Domains. In Springer INdAM Series. (pp. 43-60). Springer-Verlag Italia s.r.l..

MLA:

Bögelein, Verena, Frank Duzaar, and Christoph Scheven. "Evolutionary Problems in Non-Cylindrical Domains." Springer INdAM Series. Springer-Verlag Italia s.r.l., 2021. 43-60.

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