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Stochastic Processes and their Applications, ISSN 0304-4149, 09/2017, Volume 127, Issue 9, pp. 2961 - 3004
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
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2017, Volume 40, Issue 8, pp. 2994 - 2999
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
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
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
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
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
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
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
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
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
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
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 03/2018, Volume 2018, Issue 65, pp. 1 - 11
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
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
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
Journal Article
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