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Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 108, Issue 10, pp. 2315 - 2362
The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties... 
53C50 | Quantum field theory in curved spacetime | Theoretical, Mathematical and Computational Physics | Complex Systems | 58J45 (Primary) | 35L15 | Physics | Characteristic Cauchy problem | 58J47 | Geometry | Linear wave equations | Globally hyperbolic Lorentzian manifold | 81T20 (Secondary) | Null hypersurface | 58Z05 | Group Theory and Generalizations | DISTRIBUTIONS | SPACETIMES | PRODUCTS | HADAMARD STATES | CONSTRUCTION | FORMULA | PHYSICS, MATHEMATICAL
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 03/2019, Volume 123, pp. 201 - 228
Journal Article
Classical and Quantum Gravity, ISSN 0264-9381, 07/2012, Volume 29, Issue 14, pp. 145006 - 27
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2010, Volume 362, Issue 9, pp. 4853 - 4869
Journal Article
Analysis and PDE, ISSN 2157-5045, 2016, Volume 9, Issue 1, pp. 111 - 149
We construct Hadamard states for Klein-Gordon fields in a spacetime M-0 equal to the interior of the future lightcone C from a base point p in a globally... 
Curved spacetimes | Microlocal spectrum condition | Hadamard states | Pseudodifferential calculus | Characteristic Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | curved spacetimes | pseudodifferential calculus | QUANTUM-FIELD THEORY | characteristic Cauchy problem | microlocal spectrum condition
Journal Article
Doklady Mathematics, ISSN 1064-5624, 3/2019, Volume 99, Issue 2, pp. 149 - 151
... © The Author(s), 2019, published in Doklady Akademii Nauk, 2019, Vol. 485, No. 2. Interpolation by Sums of Series of Exponentials and Global Cauchy Problem for Convolution... 
Mathematics, general | Mathematics | MATHEMATICS | NODES | INVARIANT SUBSPACES | VALLEE-POUSSIN PROBLEM | FUNDAMENTAL PRINCIPLE | MULTIPOINT | CONVEX DOMAINS
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 06/2015, Volume 2015, Issue 175, pp. 1 - 15
We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients... 
Linear ordinary differential equation | Characteristic roots | Initial value problem | Characteristic polynomial | Oscillation | MATHEMATICS | MATHEMATICS, APPLIED | characteristic roots | oscillation | characteristic polynomial | initial value problem
Journal Article
Journal of Hyperbolic Differential Equations, ISSN 0219-8916, 09/2015, Volume 12, Issue 3, pp. 535 - 579
.... Ivrii introduced the conjecture that every effectively hyperbolic operator is strongly hyperbolic, that is the Cauchy problem for P... 
energy estimates | triple characteristics | effectively hyperbolic operators | Cauchy problem | MATHEMATICS, APPLIED | LOCAL ENERGY INTEGRALS | EQUATIONS | PHYSICS, MATHEMATICAL | Operators | Symbols | Eigenvalues | Joining | Estimates | Regularity | Factorization | Mathematics - Analysis of PDEs
Journal Article
Journal of Hyperbolic Differential Equations, ISSN 0219-8916, 12/2011, Volume 8, Issue 4, pp. 615 - 650
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 2011, Volume 95, Issue 2, pp. 151 - 193
We give a local integral formula, valid on general curved spacetimes, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin... 
Compacted spin formalism | Integral representations of solutions | Dirac equation | Characteristic Cauchy problem | MATHEMATICS | FIELDS | MATHEMATICS, APPLIED | GENERAL-RELATIVITY | EQUATIONS | NULL HYPERSURFACE | HIGHER SPIN | SPACE-TIMES
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 250, Issue 9, pp. 3652 - 3667
We give an explicit representation of the solutions of the Cauchy problem, in terms of series of hypergeometric functions, for the following class of partial differential equations with double... 
Hypergeometric equation | Singular solutions | 35C05 | 35C10 | 35A20 | 33C05 | 35L10 | MATHEMATICS | OPERATORS | MULTIPLE CHARACTERISTICS
Journal Article
Tsukuba journal of mathematics, ISSN 0387-4982, 07/2015, Volume 39, Issue 1, pp. 121 - 163
Journal Article
Letters in mathematical physics, ISSN 0377-9017, 06/2020, Volume 110, Issue 6, pp. 1391 - 1423
.... This method consists in slowing down the propagation speed of the waves to transform a characteristic initial value problem into a standard Cauchy problem. 
DECAY | Asymptotic analysis | PHYSICS, MATHEMATICAL | Conformal techniques | MAXWELL FIELDS | Characteristic initial value problem
Journal Article
Izvestiya Mathematics, ISSN 1064-5632, 2018, Volume 82, Issue 5, pp. 1019 - 1075
This paper is devoted to the global solubility of the Cauchy problem for a class of non-linear hyperbolic systems of two first-order equations with two independent variables... 
non-linear systems | many-valued solutions | quasilinear systems | characteristic uniformization | Cauchy problem | MATHEMATICS | EQUATIONS | Cauchy problems | Independent variables | Solubility | Linear equations | Nonlinear systems | Hyperbolic systems
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 10/2019, Volume 44, Issue 10, pp. 940 - 989
... where and by the interior of that is the set of points such that (see Figure 1, Section 2). In this work, we are interested with the following characteristic semi-linear Cauchy problem... 
nonlinear wave equations | null hypersurfaces | light-cone | null infinity | Goursat problem | semi-global solutions | wave maps | Characteristic Cauchy problem | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | MATHEMATICS | CAUCHY-PROBLEMS | INITIAL-VALUE PROBLEM | Minkowski space | Mathematical analysis | Formulas (mathematics) | Spacetime | Wave equations
Journal Article
MONATSHEFTE FUR MATHEMATIK, ISSN 0026-9255, 05/2020, Volume 192, Issue 1, pp. 1 - 38
We study a class of hyperbolic Cauchy problems, associated with linear operators and systems with polynomially bounded coefficients, variable multiplicities and involutive characteristics, globally defined on R-n... 
FRECHET | WAVE-FRONT SETS | Fourier integral operator | BANACH | INFINITY | MATHEMATICS | Propagation of singularities | FOURIER INTEGRAL-OPERATORS | Hyperbolic Cauchy problem | Involutive characteristics | Stochastic PDEs | Global wave-front set | EQUATION
Journal Article
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