A Framework for Nonlocal, Nonlinear Initial Value Problems

Karch G, Kaßmann M, Krupski M (2020)
SIAM Journal on Mathematical Analysis 52(3): 2383-2410.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Karch, Grzegorz; Kaßmann, MoritzUniBi ; Krupski, Milosz
Abstract / Bemerkung
We study the Cauchy problem for nonlinear, nonlocal operators that may be degenerate. Our general framework includes cases where the jump intensity is allowed to depend on the values of the solution itself, e.g., the porous medium equation with the fractional Laplacian and the parabolic fractional p-Laplacian. We show the existence and uniqueness of bounded solutions, and study their further properties. Several new examples of nonlocal, nonlinear operators are provided.
Stichworte
nonlinear diffusion; nonlocal evolution equations
Erscheinungsjahr
2020
Zeitschriftentitel
SIAM Journal on Mathematical Analysis
Band
52
Ausgabe
3
Seite(n)
2383-2410
ISSN
0036-1410
eISSN
1095-7154
Page URI
https://pub.uni-bielefeld.de/record/2945135

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Karch G, Kaßmann M, Krupski M. A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Journal on Mathematical Analysis. 2020;52(3):2383-2410.
Karch, G., Kaßmann, M., & Krupski, M. (2020). A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Journal on Mathematical Analysis, 52(3), 2383-2410. https://doi.org/10.1137/19M124143X
Karch, G., Kaßmann, M., and Krupski, M. (2020). A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Journal on Mathematical Analysis 52, 2383-2410.
Karch, G., Kaßmann, M., & Krupski, M., 2020. A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Journal on Mathematical Analysis, 52(3), p 2383-2410.
G. Karch, M. Kaßmann, and M. Krupski, “A Framework for Nonlocal, Nonlinear Initial Value Problems”, SIAM Journal on Mathematical Analysis, vol. 52, 2020, pp. 2383-2410.
Karch, G., Kaßmann, M., Krupski, M.: A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Journal on Mathematical Analysis. 52, 2383-2410 (2020).
Karch, Grzegorz, Kaßmann, Moritz, and Krupski, Milosz. “A Framework for Nonlocal, Nonlinear Initial Value Problems”. SIAM Journal on Mathematical Analysis 52.3 (2020): 2383-2410.

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