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the *Cauchy* *Problem*

"... Suppose that X is a Banach space and C is an injective operator in BX, the space of all bounded linear operators on X. In this note, a two-parameter C-semigroup regularized semigroup of operators is introduced, and some of its properties are discussed. As an application we show that the existence a ..."

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and uniqueness of solution of the 2-abstract

*Cauchy**problem*∂/∂tiut1, t2 Hiut1, t2, i 1, 2, ti> 0, u0, 0 x, x∈CDH1∩DH2 is closely related to the two-parameter C-semigroups of operators. Copyright q 2009 Mohammad Janfada. This is an open access article distributed under the Creative Commons Attribution###
*Cauchy* *problem*

"... ABSTRACT. We study uniqueness for invariant measures of the stochastic abstract Cauchy problem du(t) = Au(t) dt+ B dWH(t); t> 0; u(0) = x; where A is the generator of a C0semigroup fS(t)gt>0 on a separable real Banach space, fWH(t)gt>0 is a cylindrical Wiener process with Cameron-Martin s ..."

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ABSTRACT. We study uniqueness for invariant measures of the stochastic abstract

*Cauchy**problem*du(t) = Au(t) dt+ B dWH(t); t> 0; u(0) = x; where A is the generator of a C0semigroup fS(t)gt>0 on a separable real Banach space, fWH(t)gt>0 is a cylindrical Wiener process with Cameron###
The *Cauchy* *problem*

"... problem for the nonlinear integro-partial differential equation that describes the time evolution of sociodynamic quantities (Qualitative theory of functional equations and its application to mathematical science) ..."

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*problem*for the nonlinear integro-partial differential equation that describes the time evolution of sociodynamic quantities (Qualitative theory of functional equations and its application to mathematical science)

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ON THE *CAUCHY* *PROBLEM* IN THE

"... ABSTRACT. In this paper we shall prove the global existence of so lutions of the classical Maxwell-Chern-Simons-Higgs equations in $(2+1)$-dimensional Minkowski spacetime in the temporal gauge. We also prove that the topological solution of the Maxwell-Chern-Simons-Higgs system converges to that of ..."

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ABSTRACT. In this paper we shall prove the global existence of so lutions of the classical Maxwell-Chern-Simons-Higgs equations in $(2+1)$-dimensional Minkowski spacetime in the temporal gauge. We also prove that the topological solution of the Maxwell-Chern-Simons-Higgs system converges to that of Maxwell-Higgs system, as $\kappa $ goes to zero. Thus we reproduce the classical result by Mon-grief [6] on the global existence of the Maxwell-Klein-Gordon sys-tem in $(2+1)\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$. 1.

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*Cauchy* *problem*

"... (Communicated by the associate editor name) Abstract. We study the long-time behavior of non-negative solutions to the ..."

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(Communicated by the associate editor name) Abstract. We study the long-time behavior of non-negative solutions to the

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*Cauchy* *problem*

, 2004

"... Abstract. We find minimal regularity conditions on the coefficients of a parabolic operator, ensuring that no nontrivial solution tends to zero faster than any exponential. ..."

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Abstract. We find minimal regularity conditions on the coefficients of a parabolic operator, ensuring that no nontrivial solution tends to zero faster than any exponential.

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ON THE *CAUCHY* *PROBLEM* FOR

, 2001

"... To appear in Comunications in PDE. The dynamics for a thin, closed loop inextensible Euler’s elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order elliptic equation for its te ..."

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To appear in Comunications in PDE. The dynamics for a thin, closed loop inextensible Euler’s elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order elliptic equation for its tension. A Hasimoto transformation is used to rewrite the equations in convenient coordinates for the space and time derivatives of the tangent vector. A feature of this elastica is that it exhibits time-dependent monodromy. A frame frame parallel-transported along the elastica is in general only quasi-periodic, resulting in time-dependent boundary conditions for the coordinates. This complication is addressed by a gauge transformation, after which a contraction mapping argument can be applied. Local existence and uniqueness of elastica solutions are established for initial data in suitable Sobolev spaces. 1 1

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*Cauchy* *problem*

"... Abstract. We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1loc difference between the approximate solution and the unique entropy solution co ..."

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Abstract. We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1loc difference between the approximate solution and the unique entropy solution converges at a rate O(∆x1/11), where ∆x is the spatial mesh size. If the diffusion is linear, we get the convergence rate O(∆x1/2), the point being that the O is independent of the size of the diffusion.

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ON THE *CAUCHY* *PROBLEM* FOR HARTREE EQUATION IN

, 2012

"... Rémi Carles, Lounes Mouzaoui. On the Cauchy problem for Hartree equation in the Wiener ..."

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Rémi Carles, Lounes Mouzaoui. On the

*Cauchy**problem*for Hartree equation in the Wiener