Results 11 to 20 of about 2,922 (139)
Space Propagation of Instabilities in Zakharov Equations [PDF]
, 2007 In this paper we study an initial boundary value problem for Zakharov's equations, describing the space propagation of a laser beam entering in a plasma. We prove a strong instability result and prove that the mathematical problem is ill-posed in Sobolev
Alinhac +11 more
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Uniqueness Theorems for Goursat-Type Problems
Journal of Differential Equations, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mishnaevskii, P.A., Ramm, A.G.
openaire +2 more sources
Singularity Classes of Special 2-Flags [PDF]
, 2009 In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp).
Mormul, Piotr
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Discretization of Liouville type nonautonomous equations preserving integrals [PDF]
, 2016 The problem of constructing semi-discrete integrable analogues of the Liouville type integrable PDE is discussed. We call the semi-discrete equation a discretization of the Liouville type PDE if these two equations have a common integral.
Habibullin, Ismagil +1 more
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Fundamental Solutions of the Axial Symmetric Goursat Problem [PDF]
Journal of Nonlinear Mathematical Physics, 1996 Summary: Fundamental solutions with a given boundary condition on the characteristics of relativistic problems with axial symmetry are considered. This is the so-called Goursat problem, or zero plane formalism in Dirac's terminology, or modification of the proper time method in the Fock-Nambu-Schwinger formalism.
Borghardt, A. A. +2 more
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Contact Geometry of Hyperbolic Equations of Generic Type [PDF]
, 2008 We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampere (class 6-6), Goursat (class 6-7) and generic (class 7-7 ...
The, Dennis
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Generalized Solutions of a Periodic Goursat Problem [PDF]
Journal of Applied Analysis, 2001 Following, P. R. Garabedian (1964) and E. Goursat (1956) and the author's two papers (1995) and (1997), the Goursat problem in \(\mathbb{R}^2\) is \[ {\partial^2u\over\partial x \partial y} (x,y)= f(x,y,u(x, y));\;u(x,0)= v(x);\;u(0,y)= w(y), \] where \(f\) is a complex valued function on \(\mathbb{R}^2\times \mathbb{C}\), smooth in the four underlying
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Well-posedness of the Goursat problem and stability for point source inverse backscattering
, 2017 We show logarithmic stability for the point source inverse backscattering problem under the assumption of angularly controlled potentials. Radial symmetry implies H\"older stability.
Blåsten, Eemeli
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Amenability versus non‐exactness of dense subgroups of a compact group
Journal of the London Mathematical Society, Volume 100, Issue 2, Page 592-622, October 2019., 2019 Abstract Given a countable residually finite group, we construct a compact group K and two elements w and u of K with the following properties: The group generated by w and u3 is amenable, the group generated by w and u contains a copy of the given group, and these two groups are dense in K.
Masato Mimura
wiley +1 more source
Asymptotics to all orders of the Euler--Darboux equation in a triangle
, 2018 In Einstein's theory of relativity, the interaction of two collinearly polarized plane gravitational waves can be described by a Goursat problem for the Euler--Darboux equation in a triangular domain. In this paper, using a representation of the solution
Mauersberger, Julian
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