Results 281 to 290 of about 11,623,619 (358)
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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 $$z\left( t \right)
Ruth F. Curtain, Hans Zwart
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In Theorem 2.1.10 we saw that if A is the infinitesimal generator of a C0-semigroup T(t), the solution of the abstract homogeneous Cauchy initial value problem $$\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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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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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. B. Nersesian
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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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Fractional Abstract Cauchy Problems
Integral Equations and Operator Theory, 2011Fractional abstract Cauchy problems with order \(\alpha \in (1,2)\) are studied. Existence and uniqueness of mild solutions and strong solutions of the inhomogeneous fractional Cauchy problem are established.
Li, Kexue, Peng, Jigen
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1991
The contemporary state of the question for the correctness of the Cauchy problem is exposed for differential and pseudo-differential operators with non-homogeneous symbols. Ch.1,2 are devoted to constant coefficients, criteria for the correctness of the Cauchy problem in spaces of functions and distributions of power and exponential decrease and ...
Volevich, L. R., Gindikin, S. G.
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The contemporary state of the question for the correctness of the Cauchy problem is exposed for differential and pseudo-differential operators with non-homogeneous symbols. Ch.1,2 are devoted to constant coefficients, criteria for the correctness of the Cauchy problem in spaces of functions and distributions of power and exponential decrease and ...
Volevich, L. R., Gindikin, S. G.
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1984
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations.
Hector O. Fattorini, Adalbert Kerber
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This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations.
Hector O. Fattorini, Adalbert Kerber
+4 more sources