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Jiang G, Mao T.
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Shariff MHBM.
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In Theorem 2.1.10 we saw that if A is the infinitesimal generator of a C0-semigroup T(t), the solution of the abstract homogeneous Cauchy initial value problem $$\begin{array}{*{20}{c}}{\dot z\left( t \right) = Az\left( t \right),}&{t \geqslant 0,}&{z\left( 0 \right) = {z_0} \in D\left( A \right)}\end{array}$$ is given by $$z\left( t \right)
Ruth F. Curtain, Hans Zwart
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On the Cauchy problem for a class of differential inclusions with applications
Applicable Analysis, 2020Our main result is the following: let be a multifunction, and assume that there exists a neglegible subset , satisfying a certain geometrical condition, such that the restriction of F to is bounded, lower semicontinuous with non-empty closed values, and ...
Paolo Cubiotti, Jen-Chih Yao
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Fractional derivatives and cauchy problem for differential equations of fractional order
, 2020Editorial Note: This is a paper by M.M. Djrbashian and A.B. Nersesian of 1968, that was published in Russian. There is a constant interest to Djrbashian’s contributions to the topic of fractional calculus and theory of Mittag-Leffler function ...
M.M. Dzherbashian, A. Nersesian
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On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data
, 2020We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in $$L^2$$ L 2 .
T. Alazard, Quoc-Hung Nguyen
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Paralinearization of the Muskat Equation and Application to the Cauchy Problem
Archive for Rational Mechanics and Analysis, 2019We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-posedness of the Cauchy problem for rough initial data, in homogeneous Sobolev
T. Alazard, O. Lazar
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