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May/June 2018 Existence of entropy solutions to a doubly nonlinear integro-differential equation
Martin Scholtes, Petra Wittbold
Differential Integral Equations 31(5/6): 465-496 (May/June 2018).

Abstract

We consider a class of doubly nonlinear history-dependent problems associated with the equation $$ \partial_{t}k\ast(b(v)- b(v_{0})) = \text{div}\, a(x,Dv) + f . $$ Our assumptions on the kernel $k$ include the case $k(t) = t^{-\alpha}/\Gamma(1-\alpha)$, in which case the left-hand side becomes the fractional derivative of order $\alpha\in (0,1)$ in the sense of Riemann-Liouville. Existence of entropy solutions is established for general $L^{1}-$data and Dirichlet boundary conditions. Uniqueness of entropy solutions has been shown in a previous work.

Citation

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Martin Scholtes. Petra Wittbold. "Existence of entropy solutions to a doubly nonlinear integro-differential equation." Differential Integral Equations 31 (5/6) 465 - 496, May/June 2018.

Information

Published: May/June 2018
First available in Project Euclid: 23 January 2018

zbMATH: 06861587
MathSciNet: MR3749217

Subjects:
Primary: 35D99, 45D05, 45K05, 47J35

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 5/6 • May/June 2018
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