Stochastic Processes and their Applications, ISSN 0304-4149, 09/2017, Volume 127, Issue 9, pp. 2961 - 3004

We introduce the notion of pathwise entropy solutions for a class of degenerate parabolic–hyperbolic equations with non-isotropic nonlinearity and fluxes with...

Stochastic scalar conservation laws | Averaging lemma | Parabolic–hyperbolic equations | Random attractor | Invariant measure | Random dynamical systems | EXISTENCE | POROUS-MEDIA EQUATIONS | LARGE-TIME BEHAVIOR | CAUCHY-PROBLEM | STATISTICS & PROBABILITY | MULTIPLE ROUGH FLUXES | DEPENDENCE | UNIQUENESS | ENTROPY SOLUTIONS | Parabolic-hyperbolic equations | PARTIAL-DIFFERENTIAL-EQUATIONS | SCALAR CONSERVATION-LAWS | Environmental law | Analysis

Stochastic scalar conservation laws | Averaging lemma | Parabolic–hyperbolic equations | Random attractor | Invariant measure | Random dynamical systems | EXISTENCE | POROUS-MEDIA EQUATIONS | LARGE-TIME BEHAVIOR | CAUCHY-PROBLEM | STATISTICS & PROBABILITY | MULTIPLE ROUGH FLUXES | DEPENDENCE | UNIQUENESS | ENTROPY SOLUTIONS | Parabolic-hyperbolic equations | PARTIAL-DIFFERENTIAL-EQUATIONS | SCALAR CONSERVATION-LAWS | Environmental law | Analysis

Journal Article

Mathematical Notes, ISSN 0001-4346, 9/2017, Volume 102, Issue 3, pp. 378 - 395

A problem with inhomogeneous boundary and initial conditions is studied for an inhomogeneous equation of mixed parabolic-hyperbolic type in a rectangular...

existence and uniqueness of solutions | inverse problem | parabolic-hyperbolic equation | initial boundary-value problem | Mathematics, general | spectral analysis | Mathematics | small denominator | MATHEMATICS

existence and uniqueness of solutions | inverse problem | parabolic-hyperbolic equation | initial boundary-value problem | Mathematics, general | spectral analysis | Mathematics | small denominator | MATHEMATICS

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2017, Volume 40, Issue 8, pp. 2994 - 2999

In this work, we investigate a boundary problem with non‐local conditions for mixed parabolic–hyperbolic‐type equation with three lines of type changing with...

parabolic–hyperbolic‐type equation | Volterra integral equation | Green's function | Caputo fractional derivative | mixed‐type equation | parabolic–hyperbolic-type equation | mixed-type equation | MATHEMATICS, APPLIED | PARABOLIC-HYPERBOLIC EQUATION | BOUNDARY-VALUE PROBLEM | parabolic-hyperbolic-type equation | Green's functions | Derivatives | Integrals | Volterra integral equations | Cauchy problem

parabolic–hyperbolic‐type equation | Volterra integral equation | Green's function | Caputo fractional derivative | mixed‐type equation | parabolic–hyperbolic-type equation | mixed-type equation | MATHEMATICS, APPLIED | PARABOLIC-HYPERBOLIC EQUATION | BOUNDARY-VALUE PROBLEM | parabolic-hyperbolic-type equation | Green's functions | Derivatives | Integrals | Volterra integral equations | Cauchy problem

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 03/2017, Volume 58, Issue 2, pp. 227 - 231

We state a new nonlocal boundary value problem for a mixed parabolic-hyperbolic equation. The equation is of the first kind, i.e., the curve on which the...

nonlocal boundary condition | Green’s function | parabolic-hyperbolic equation | Frankl problem | MATHEMATICS | BOUNDARY-VALUE-PROBLEM | Green's function | RECTANGULAR DOMAIN | TRICOMI

nonlocal boundary condition | Green’s function | parabolic-hyperbolic equation | Frankl problem | MATHEMATICS | BOUNDARY-VALUE-PROBLEM | Green's function | RECTANGULAR DOMAIN | TRICOMI

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2019, Volume 42, Issue 11, pp. 3865 - 3876

In this paper, we study an analog of the Gellerstedt problem for the third‐order loaded equation with boundary conditions on nonparallel characteristics in the...

gluing conditions | integral equation | equations of mixed type | boundary value problems | loaded equation | MATHEMATICS, APPLIED | PARABOLIC-HYPERBOLIC EQUATION | PARTIAL-DIFFERENTIAL-EQUATIONS | MIXED-TYPE | Boundary conditions

gluing conditions | integral equation | equations of mixed type | boundary value problems | loaded equation | MATHEMATICS, APPLIED | PARABOLIC-HYPERBOLIC EQUATION | PARTIAL-DIFFERENTIAL-EQUATIONS | MIXED-TYPE | Boundary conditions

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2019

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 05/2012, Volume 252, Issue 9, pp. 4719 - 4741

The aim of this paper is to prove the well-posedness (existence and uniqueness) of entropy solutions to the general anisotropic degenerate parabolic–hyperbolic...

Degenerate parabolic–hyperbolic equation | Uniqueness | Anisotropic | Homogeneous boundary condition | Boundary entropy–entropy flux triple | Doubling variables device | Existence | 2ND-ORDER | APPROXIMATIONS | STABILITY | ENTROPY SOLUTIONS | MATHEMATICS | LAWS | BOUNDARY-VALUE-PROBLEM | COEFFICIENTS | CONVERGENCE | Degenerate parabolic-hyperbolic equation | ADAPTIVE MULTIRESOLUTION SCHEMES | Boundary entropy-entropy flux triple | Invisibility | Anisotropy | Analysis

Degenerate parabolic–hyperbolic equation | Uniqueness | Anisotropic | Homogeneous boundary condition | Boundary entropy–entropy flux triple | Doubling variables device | Existence | 2ND-ORDER | APPROXIMATIONS | STABILITY | ENTROPY SOLUTIONS | MATHEMATICS | LAWS | BOUNDARY-VALUE-PROBLEM | COEFFICIENTS | CONVERGENCE | Degenerate parabolic-hyperbolic equation | ADAPTIVE MULTIRESOLUTION SCHEMES | Boundary entropy-entropy flux triple | Invisibility | Anisotropy | Analysis

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 08/2016, Volume 1759, Issue 1

In the paper a new non-local boundary value problem for an equation of the parabolic-hyperbolic type is formulated. This equation is of the first kind, that...

Nonlocal boundary conditions | Frankl problem | Greens function | Equation of the parabolic-hyperbolic type | Boundary value problems

Nonlocal boundary conditions | Frankl problem | Greens function | Equation of the parabolic-hyperbolic type | Boundary value problems

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 01/2015, Volume 291, pp. 31 - 44

We prove the existence of a global attractor and estimate its dimension for a general family of third-order quasilinear parabolic–hyperbolic equations...

Quasilinear parabolic–hyperbolic equations | Nonlinearly viscoelastic rods | Dimension of attractors | Quasilinear parabolic-hyperbolic equations | MATHEMATICS, APPLIED | PHASE | PHYSICS, MULTIDISCIPLINARY | NAVIER-STOKES | MANIFOLDS | PHYSICS, MATHEMATICAL

Quasilinear parabolic–hyperbolic equations | Nonlinearly viscoelastic rods | Dimension of attractors | Quasilinear parabolic-hyperbolic equations | MATHEMATICS, APPLIED | PHASE | PHYSICS, MULTIDISCIPLINARY | NAVIER-STOKES | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 08/2016, Volume 1759, Issue 1

In the present paper, a spectral problem for an operator of parabolic-hyperbolic type of I kind with non-classical boundary conditions is considered. The...

Boundary condition with shift | Spectral problem | Equation of parabolic-hyperbolic type | Eigenvalues | Boundary conditions | Eigen values

Boundary condition with shift | Spectral problem | Equation of parabolic-hyperbolic type | Eigenvalues | Boundary conditions | Eigen values

Journal Article

Results in Mathematics, ISSN 1422-6383, 06/2017, Volume 71, Issue 3-4, pp. 1235 - 1257

In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for a mixed parabolic-hyperbolic type...

parabolic–hyperbolic equation | Green’s function | Caputo derivative | transmitting condition | MATHEMATICS | MATHEMATICS, APPLIED | parabolic-hyperbolic equation | BOUNDARY-VALUE PROBLEM | Green's function

parabolic–hyperbolic equation | Green’s function | Caputo derivative | transmitting condition | MATHEMATICS | MATHEMATICS, APPLIED | parabolic-hyperbolic equation | BOUNDARY-VALUE PROBLEM | Green's function

Journal Article

Asian-European Journal of Mathematics, ISSN 1793-5571, 2014, Volume 7, Issue 2

Journal Article

CLASSICAL AND QUANTUM GRAVITY, ISSN 0264-9381, 09/2019, Volume 36, Issue 17, p. 175005

In this paper we investigate the parabolic-hyperbolic formulation of the vacuum constraint equations introduced by Racz with a view to constructing multiple...

QUANTUM SCIENCE & TECHNOLOGY | binary black hole initial data | PHYSICS, MULTIDISCIPLINARY | asymptotics | ASTRONOMY & ASTROPHYSICS | constraints | parabolic-hyperbolic formulation | PHYSICS, PARTICLES & FIELDS | Physics - General Relativity and Quantum Cosmology

QUANTUM SCIENCE & TECHNOLOGY | binary black hole initial data | PHYSICS, MULTIDISCIPLINARY | asymptotics | ASTRONOMY & ASTROPHYSICS | constraints | parabolic-hyperbolic formulation | PHYSICS, PARTICLES & FIELDS | Physics - General Relativity and Quantum Cosmology

Journal Article

Russian Mathematics, ISSN 1066-369X, 07/2017, Volume 61, Issue 7, pp. 49 - 57

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.3103/S1066369X17070076 We study...

equation of mixed parabolic-hyperbolic type of second and higher orders | fixed sign solution | polycaloric equation | maximum principle

equation of mixed parabolic-hyperbolic type of second and higher orders | fixed sign solution | polycaloric equation | maximum principle

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 10

This research work is devoted to investigations of the existence and uniqueness of the solution of a non-local boundary value problem with discontinuous...

parabolic-hyperbolic type | discontinuous matching condition | non-local condition | Mathematics | 35M10 | Caputo fractional derivative | loaded equation | existence and uniqueness of solution | integral equations | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | integral energy | Mathematics, general | Partial Differential Equations | MATHEMATICS, APPLIED | CALCULUS | DIFFERENTIAL-EQUATIONS | MATHEMATICS | DYNAMICS | Matching | Boundary value problems | Difference equations | Integrals | Integral equations | Mathematical analysis | Uniqueness | Derivatives

parabolic-hyperbolic type | discontinuous matching condition | non-local condition | Mathematics | 35M10 | Caputo fractional derivative | loaded equation | existence and uniqueness of solution | integral equations | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | integral energy | Mathematics, general | Partial Differential Equations | MATHEMATICS, APPLIED | CALCULUS | DIFFERENTIAL-EQUATIONS | MATHEMATICS | DYNAMICS | Matching | Boundary value problems | Difference equations | Integrals | Integral equations | Mathematical analysis | Uniqueness | Derivatives

Journal Article

Science China Mathematics, ISSN 1674-7283, 5/2019, Volume 62, Issue 5, pp. 839 - 852

In this article, we prove a general existence theorem for a class of nonlinear degenerate parabolichyperbolic equations. Since the regions of parabolicity and...

energy methods | vanishing viscosity methods | 35L60 | Mathematics | parabolic-hyperbolic equations | Applications of Mathematics | 35K55 | 35K65 | MATHEMATICS | MATHEMATICS, APPLIED

energy methods | vanishing viscosity methods | 35L60 | Mathematics | parabolic-hyperbolic equations | Applications of Mathematics | 35K55 | 35K65 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 03/2018, Volume 2018, Issue 65, pp. 1 - 11

In this article we study spectral properties of non-local boundary value problem for an equation of parabolic-hyperbolic type. The non-local condition binds...

Parabolic-hyperbolic equation | Eigenvalues | Equation of the mixed type | Frankl type problem | Spectral properties | Non-local boundary value problem | LAVRENTEV-BITSADZE EQUATION | MATHEMATICS, APPLIED | eigenvalues | TRICOMI PROBLEM | BOUNDARY-VALUE PROBLEM | VOLTERRA PROPERTY | EIGENFUNCTIONS | MATHEMATICS | parabolic-hyperbolic equation | OPERATOR | spectral properties

Parabolic-hyperbolic equation | Eigenvalues | Equation of the mixed type | Frankl type problem | Spectral properties | Non-local boundary value problem | LAVRENTEV-BITSADZE EQUATION | MATHEMATICS, APPLIED | eigenvalues | TRICOMI PROBLEM | BOUNDARY-VALUE PROBLEM | VOLTERRA PROPERTY | EIGENFUNCTIONS | MATHEMATICS | parabolic-hyperbolic equation | OPERATOR | spectral properties

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 2/2019, Volume 236, Issue 6, pp. 603 - 640

We consider initial-boundary-value problems for three classes of inhomogeneous degenerate equations of mixed parabolic-hyperbolic type: mixed-type equations...

mixed parabolic-hyperbolic equation | spectral method | initial-boundary-value problem | uniqueness | series | uniform convergence | existence | small denominators | Mathematics, general | Mathematics | 35M10 | 35Q60

mixed parabolic-hyperbolic equation | spectral method | initial-boundary-value problem | uniqueness | series | uniform convergence | existence | small denominators | Mathematics, general | Mathematics | 35M10 | 35Q60

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, ISSN 1531-3492, 03/2019, Volume 24, Issue 3, pp. 1243 - 1258

In this work, we consider a dynamical system generated by a parabolic-hyperbolic equation with non-local boundary conditions. The optimal control problem for...

MATHEMATICS, APPLIED | non-local boundary conditions | optimal control | distributed systems | parabolic-hyperbolic equations | Dynamical system | quadratic criterion

MATHEMATICS, APPLIED | non-local boundary conditions | optimal control | distributed systems | parabolic-hyperbolic equations | Dynamical system | quadratic criterion

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 01/2014, Volume 2014, Issue 14, pp. 1 - 6

In the present work we investigate the Tricomi problem with an integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional...

Parabolic-hyperbolic equation | Green's function | Caputo fractional derivative | Tricomi problem | MATHEMATICS | MATHEMATICS, APPLIED

Parabolic-hyperbolic equation | Green's function | Caputo fractional derivative | Tricomi problem | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

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