The Experts below are selected from a list of 81 Experts worldwide ranked by ideXlab platform
Joshua Feinberg - One of the best experts on this subject based on the ideXlab platform.
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does the complex deformation of the Riemann Equation exhibit shocks
Journal of Physics A, 2008Co-Authors: Carl M Bender, Joshua FeinbergAbstract:The Riemann Equation ut + uux = 0, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This Equation is symmetric. A one-parameter -invariant complex deformation of this Equation, ut ? iu(iux) = 0 ( real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless is an odd integer. When is an odd integer, the shock-formation time is calculated explicitly.
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does the complex deformation of the Riemann Equation exhibit shocks
arXiv: High Energy Physics - Theory, 2007Co-Authors: Carl M Bender, Joshua FeinbergAbstract:The Riemann Equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This Equation is $\cP\cT$ symmetric. A one-parameter $\cP\cT$-invariant complex deformation of this Equation, $u_t-iu(iu_x)^\epsilon= 0$ ($\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\epsilon$ is an odd integer.
Katrin Wehrheim - One of the best experts on this subject based on the ideXlab platform.
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space valued Cauchy-Riemann Equations with totally real boundary conditions
2013Co-Authors: Katrin WehrheimAbstract:The main purpose of this paper is to give a general regularity result for Cauchy-Riemann Equations in complex Banach spaces with totally real boundary conditions. The usual elliptic L p-regularity results hold true under one crucial assumption: The Banach space is isomorphic to a closed subspace of an L p-space. (Equivalently, the totally real submanifold is modelled on a closed subspace of an L p-space.) Some minor corrections are in order on the Sobolev arithmetic in the estimates. Secondly, we describe a class of examples of such totally real submanifolds, namely gauge invariant Lagrangian submanifolds in the space of connections over a Riemann surface. These pose natural boundary conditions for the anti-self-duality Equation on 4-manifolds with a boundary space-time splitting, leading towards the definition of a Floer homology for 3-manifolds with boundary, which is the first step in a program by Salamon for the proof of the Atiyah-Floer conjecture. The principal part of such a boundary value problem is an example of a Banach space valued Cauchy-Riemann Equation with totally real boundary condition.
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banach space valued cauchy Riemann Equations with totally real boundary conditions
Communications in Contemporary Mathematics, 2004Co-Authors: Katrin WehrheimAbstract:The main purpose of this paper is to give a general regularity result for Cauchy–Riemann Equations in complex Banach spaces with totally real boundary conditions. The usual elliptic Lp-regularity results hold true under one crucial assumption: The Banach space is isomorphic to a closed subspace of an Lp-space. (Equivalently, the totally real submanifold is modelled on a closed subspace of an Lp-space.) Secondly, we describe a class of examples of such totally real submanifolds, namely gauge invariant Lagrangian submanifolds in the space of connections over a Riemann surface. These pose natural boundary conditions for the anti-self-duality Equation on 4-manifolds with a boundary space-time splitting, leading towards the definition of a Floer homology for 3-manifolds with boundary, which is the first step in a program by Salamon for the proof of the Atiyah–Floer conjecture. The principal part of such a boundary value problem is an example of a Banach space valued Cauchy–Riemann Equation with totally real boundary condition.
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banach space valued cauchy Riemann Equations with totally real boundary conditions
arXiv: Analysis of PDEs, 2004Co-Authors: Katrin WehrheimAbstract:The main purpose of this paper is to give a general regularity result for Cauchy-Riemann Equations in complex Banach spaces with totally real boundary conditions. The usual elliptic $L^p$-regularity results hold true under one crucial assumption: The totally real submanifold has to be modelled on an $L^p$-space or a closed subspace thereof. Secondly, we describe a class of examples of such totally real submanifolds, namely gauge invariant Lagrangian submanifolds in the space of connections over a Riemann surface. These pose natural boundary conditions for the anti-self-duality Equation on 4-manifolds with a boundary space-time splitting, leading towards the definition of a Floer homology for 3-manifolds with boundary, which is the first step in a program by Salamon for the proof of the Atiyah-Floer conjecture. The principal part of such a boundary value problem is an example of a Banach space valued Cauchy-Riemann Equation with totally real boundary condition.
Timergaliev S. - One of the best experts on this subject based on the ideXlab platform.
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On the existence of solutions of one nonlinear boundary-value problem for shallow shells of Timoshenko type with simply supported edges
2020Co-Authors: Timergaliev S., Kharasova L.Abstract:© Published under licence by IOP Publishing Ltd.Solvability of one system of nonlinear second order partial differential Equations with given initial conditions is considered in an arbitrary field. Reduction of the initial system of Equations to one nonlinear operator Equation is used to study the problem. The solvability is established with the use of the principle of contracting mappings. The method used in these studies is based on the integral representations for the displacements. These representations are constructed with the use of general solutions to the inhomogeneous Cauchy-Riemann Equation
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On the existence of solutions to geometrically nonlinear problems for shallow Timoshenko-type shells with free edges
2020Co-Authors: Timergaliev S.Abstract:In the paper we investigate the solvability of the boundary-value problems for shallow isotropic elastic shells within the framework of Timoshenko's shearmodel. The considered problems are nonlinear geometrically and linear physically. The method of studying consists in reducing the initial system of equilibrium Equations to one nonlinear differential Equation with respect to deflections. In doing so integral representations for the tangential displacements and angles of rotation play a significant role. The representations are deduced by making use of general solutions to the inhomogeneous Cauchy-Riemann Equation. The solvability is established by the principle of contracting mappings. © 2014 Allerton Press, Inc
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Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges
2020Co-Authors: Timergaliev S., Uglov A., Kharasova L.Abstract:© 2015, Allerton Press, Inc. We study solvability of a geometrically nonlinear, physically linear boundary-value problems for elastic shallow homogeneous isotropic shells with pivotally supported edges in the framework of S. P. Timoshenko’s shear model. The purpose of work is the proof of the theorem on existence of solutions. Research method consists in reducing the original system of equilibrium Equations to one nonlinear differential Equation for the deflection. The method is based on integral representations for displacements, which are built with the help of the general solutions of the nonhomogeneous Cauchy-Riemann Equation. The solvability of Equation relative to deflection is established with the use of principle of contraction mappings
Kharasova L. - One of the best experts on this subject based on the ideXlab platform.
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On the existence of solutions of one nonlinear boundary-value problem for shallow shells of Timoshenko type with simply supported edges
2020Co-Authors: Timergaliev S., Kharasova L.Abstract:© Published under licence by IOP Publishing Ltd.Solvability of one system of nonlinear second order partial differential Equations with given initial conditions is considered in an arbitrary field. Reduction of the initial system of Equations to one nonlinear operator Equation is used to study the problem. The solvability is established with the use of the principle of contracting mappings. The method used in these studies is based on the integral representations for the displacements. These representations are constructed with the use of general solutions to the inhomogeneous Cauchy-Riemann Equation
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Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges
2020Co-Authors: Timergaliev S., Uglov A., Kharasova L.Abstract:© 2015, Allerton Press, Inc. We study solvability of a geometrically nonlinear, physically linear boundary-value problems for elastic shallow homogeneous isotropic shells with pivotally supported edges in the framework of S. P. Timoshenko’s shear model. The purpose of work is the proof of the theorem on existence of solutions. Research method consists in reducing the original system of equilibrium Equations to one nonlinear differential Equation for the deflection. The method is based on integral representations for displacements, which are built with the help of the general solutions of the nonhomogeneous Cauchy-Riemann Equation. The solvability of Equation relative to deflection is established with the use of principle of contraction mappings
Joaquim Ortegacerda - One of the best experts on this subject based on the ideXlab platform.
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pointwise estimates for the bergman kernel of the weighted fock space
Journal of Geometric Analysis, 2009Co-Authors: Jordi Marzo, Joaquim OrtegacerdaAbstract:We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in L 2(e −2φ ) where φ is a subharmonic function with Δφ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann Equation and we characterize the compactness of this operator in terms of Δφ.
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pointwise estimates for the bergman kernel of the weighted fock space
arXiv: Complex Variables, 2008Co-Authors: Jordi Marzo, Joaquim OrtegacerdaAbstract:We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann Equation and we characterize the compactness of this operator in terms of $\Delta \phi$.
