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

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

We study the Cauchy problem for effectively hyperbolic operators P with principal symbol p(t,x,τ,ξ...

Effectively hyperbolic operators | Energy estimates | Triple characteristics | Cauchy problem | MATHEMATICS | COUNTEREXAMPLES | MATHEMATICS, APPLIED | LOCAL ENERGY INTEGRALS | EQUATIONS | FEFFERMAN-PHONG INEQUALITY | Analysis of PDEs | Mathematics

Effectively hyperbolic operators | Energy estimates | Triple characteristics | Cauchy problem | MATHEMATICS | COUNTEREXAMPLES | MATHEMATICS, APPLIED | LOCAL ENERGY INTEGRALS | EQUATIONS | FEFFERMAN-PHONG INEQUALITY | Analysis of PDEs | Mathematics

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 07/2012, Volume 29, Issue 14, pp. 145006 - 27

We review various aspects of the characteristic initial-value problem for the Einstein equations, presenting new approaches to some of the issues arising.

EXISTENCE | EINSTEIN EQUATIONS | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | ISOLATED SYSTEMS | DES EQUATIONS DEINSTEIN | CHARACTERISTIC CONE | HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | INITIAL-VALUE-PROBLEM | SPACE-TIMES | VACUUM FIELD-EQUATIONS | PHYSICS, PARTICLES & FIELDS | Einstein equations | Quantum gravity | Cauchy problem | Physics - General Relativity and Quantum Cosmology

EXISTENCE | EINSTEIN EQUATIONS | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | ISOLATED SYSTEMS | DES EQUATIONS DEINSTEIN | CHARACTERISTIC CONE | HYPERSURFACES | ASTRONOMY & ASTROPHYSICS | INITIAL-VALUE-PROBLEM | SPACE-TIMES | VACUUM FIELD-EQUATIONS | PHYSICS, PARTICLES & FIELDS | Einstein equations | Quantum gravity | Cauchy problem | Physics - General Relativity and Quantum Cosmology

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2010, Volume 362, Issue 9, pp. 4853 - 4869

In this paper we deal with the Cauchy problem for evolution equations with real characteristics...

Mathematical theorems | Variable coefficients | Eigenvalues | Scalars | Mathematics | Coefficients | Sobolev spaces | Factorization | Cauchy problem | Continuous functions | Evolution equations with real characteristics | SCHRODINGER TYPE EQUATIONS | MATHEMATICS | NON-LIPSCHITZ COEFFICIENTS

Mathematical theorems | Variable coefficients | Eigenvalues | Scalars | Mathematics | Coefficients | Sobolev spaces | Factorization | Cauchy problem | Continuous functions | Evolution equations with real characteristics | SCHRODINGER TYPE EQUATIONS | MATHEMATICS | NON-LIPSCHITZ COEFFICIENTS

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

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

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

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

Novi Sad Journal of Mathematics, ISSN 1450-5444, 2014, Volume 44, Issue 1, pp. 201 - 223

Journal Article

Journal of computational physics, ISSN 0021-9991, 2020, Volume 401, p. 109028

•Explicit explanation for the derivation of the asymptotic behavior for the perturbation ψ(t) is clearly provided.•Numerical quantities are newly compared to...

Projection method | BDF3 | Navier–Stokes equations | Backward semi-Lagrangian method | Cauchy problem | 2ND-ORDER | ORDER CHARACTERISTICS/FINITE ELEMENTS | DIFFUSION-REACTION PROBLEMS | TIME | SIMULATION | PHYSICS, MATHEMATICAL | NUMERICAL-ANALYSIS | FLOW | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENT | Navier-Stokes equations | SEMI-LAGRANGIAN SCHEME | Interpolation | Computational fluid dynamics | Cauchy problems | Mathematical analysis | Fluid flow | Performance enhancement | Error correction | Formulas (mathematics)

Projection method | BDF3 | Navier–Stokes equations | Backward semi-Lagrangian method | Cauchy problem | 2ND-ORDER | ORDER CHARACTERISTICS/FINITE ELEMENTS | DIFFUSION-REACTION PROBLEMS | TIME | SIMULATION | PHYSICS, MATHEMATICAL | NUMERICAL-ANALYSIS | FLOW | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENT | Navier-Stokes equations | SEMI-LAGRANGIAN SCHEME | Interpolation | Computational fluid dynamics | Cauchy problems | Mathematical analysis | Fluid flow | Performance enhancement | Error correction | Formulas (mathematics)

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

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

... that the Cauchy problem for P is well-posed in the Gevrey class 1 <= s < 4 for any lower order term...

Gevrey well-posedness | non-effectively hyperbolic operators | Hamilton map and flow | Cauchy problem | double characteristics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | OSCILLATOR | Manifolds | Operators | Vices | Symbols | Blocking | Well posed problems | Optimization

Gevrey well-posedness | non-effectively hyperbolic operators | Hamilton map and flow | Cauchy problem | double characteristics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | OSCILLATOR | Manifolds | Operators | Vices | Symbols | Blocking | Well posed problems | Optimization

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

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

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

Novi Sad Journal of Mathematics, ISSN 1450-5444, 2016, Volume 46, Issue 2, pp. 163 - 180

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

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

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

Novi Sad Journal of Mathematics, ISSN 1450-5444, 2011, Volume 41, Issue 1, pp. 85 - 121

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

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

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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