Results 141 to 150 of about 11,284,175 (207)

The Cauchy Problem

Introduction to Infinite-Dimensional Systems Theory, 1995
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
openaire   +3 more sources

On the Cauchy problem for a class of differential inclusions with applications

Applicable Analysis, 2020
Our 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
semanticscholar   +1 more source

Fractional derivatives and cauchy problem for differential equations of fractional order

, 2020
Editorial 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
semanticscholar   +1 more source

On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

, 2020
We 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
semanticscholar   +1 more source

Paralinearization of the Muskat Equation and Application to the Cauchy Problem

Archive for Rational Mechanics and Analysis, 2019
We 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
semanticscholar   +1 more source

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