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Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 05/2017, Volume 33, Issue 3, pp. 868 - 884
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 1, pp. 817 - 836
The article introduces a new general solution to a family of loaded ordinary differential equations and discusses its properties. It provides necessary and... 
General solution | Solvability criteria | Algorithm | Loaded hyperbolic equations | MATHEMATICS | MATHEMATICS, APPLIED | 2 INDEPENDENT VARIABLES | DIFFERENTIAL-EQUATIONS
Journal Article
Advances in Water Resources, ISSN 0309-1708, 2011, Volume 34, Issue 9, pp. 1195 - 1206
► We describe the GeoClaw software for two-dimensional depth-averaged equations for geophysical flow problems. ► GeoClaw uses high-resolution shock-capturing... 
Hyperbolic equations | Adaptive refinement | Numerical flow modeling | Finite volume methods | Depth-averaged equations | 3-DIMENSIONAL TERRAIN | WATER RESOURCES | MODEL | FINITE-VOLUME METHODS | SHALLOW-WATER EQUATIONS | AVALANCHES | WAVE-PROPAGATION ALGORITHMS | Software | Freeware | Wave propagation | Geophysics | Mathematical models | Source code | Computer programs | Drying
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 19, pp. 7426 - 7451
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
Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 1, pp. 427 - 444
We establish a new Carleman inequality for linear Cahn–Hilliard type equation when the norms of right hand sides are in Sobolev spaces of negative orders, and... 
Global Carleman estimate | Cahn–Hilliard type equation | Null controllability | Unique Continuation Property | MATHEMATICS | Cahn Hilliard type equation | HEAT-EQUATION | APPROXIMATE CONTROLLABILITY | HYPERBOLIC-EQUATIONS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 9, pp. 4115 - 4124
We consider the second order Cauchy problem where is a continuous function, and is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It... 
Degenerate hyperbolic equation | Continuity modulus | Gevrey spaces | Integro-differential hyperbolic equation | Uniqueness | Kirchhoff equations | MATHEMATICS | MATHEMATICS, APPLIED | SOLVABILITY
Journal Article
SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2016, Volume 76, Issue 4, pp. 1658 - 1682
We analyze a one-dimensional (1D) model of molecules diffusing along a line of N cells that are connected via stochastically gated gap junctions. Each gate... 
Piecewise determinist ic PDEs | Channel permeability | Diffusion | Gap junctions | gap junctions | APPROXIMATE TRAVELING-WAVES | MATHEMATICS, APPLIED | diffusion | VOLTAGE | channel permeability | CALCIUM WAVES | NOISE | MODEL | ION-CHANNEL STOCHASTICITY | ASTROCYTES | NEURONS | REACTION-HYPERBOLIC EQUATIONS | INOSITOL-TRISPHOSPHATE | piecewise deterministic PDEs
Journal Article
Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2018, Volume 19, Issue 9, pp. 1525 - 1530
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2018, Volume 41, Issue 7, pp. 2639 - 2653
This paper deals with the energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear... 
infinite blow‐up | logarithmic nonlinear | source | energy decay estimates | strong damping | wave equation | infinite blow-up | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | HYPERBOLIC-EQUATIONS | Dirichlet problem | Estimates | Decay | Wave equations
Journal Article
Chaos, Solitons and Fractals, ISSN 0960-0779, 2009, Volume 41, Issue 3, pp. 1448 - 1453
In this work, the well known variational iteration method is used for solving the one-dimensional wave equation that combines classical and integral boundary... 
NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | HYPERBOLIC EQUATION | APPROXIMATE SOLUTION | PARABOLIC EQUATION | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE | Methods | Universities and colleges
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 230, Issue 2, pp. 626 - 632
In this paper, we propose a three level compact difference scheme of for the difference solution of a two-dimensional second-order non-homogeneous linear... 
High accuracy | Compact difference scheme | Stability analysis | Linear hyperbolic equation | MATHEMATICS, APPLIED | ADI METHOD | VARIABLE-COEFFICIENTS
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 3/2018, Volume 18, Issue 1, pp. 105 - 125
In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we... 
Analysis | Mathematics | MATHEMATICS | DISSIPATION | MATHEMATICS, APPLIED | NONEXISTENCE | GLOBAL EXISTENCE | STABILIZATION | EXPONENTIAL DECAY | PETROVSKY | WAVE-EQUATION | HYPERBOLIC-EQUATIONS | BOUNDARY
Journal Article
DIFFERENTIAL AND INTEGRAL EQUATIONS, ISSN 0893-4983, 11/2016, Volume 29, Issue 11-12, pp. 1139 - 1166
In this paper, we discuss the Cauchy problem for a degenerate parabolic-hyperbolic equation with a multiplicative noise. We focus on the existence of a... 
EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | SCALAR CONSERVATION-LAWS | HYPERBOLIC EQUATIONS | FORMULATION
Journal Article
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, ISSN 1991-8615, 03/2016, Volume 20, Issue 1, pp. 65 - 73
We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat... 
nonlocal conditions | the problem with displacement | hyperbolic equation
Journal Article
Materials Research, ISSN 1516-1439, 12/2015, Volume 18, Issue suppl 2, pp. 193 - 199
Fique is a plant native of Colombia with fibers extracted from its leaves presenting relevant physical characteristics and mechanical properties for possible... 
Elastic modulus | Hyperbolic equation | Weibull analysis | Fique fiber | VEGETABLE FIBERS | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | COMPOSITES | weibull analysis | hyperbolic equation | MECHANICAL-PROPERTIES | GLASS | NATURAL FIBERS | BIOFIBRES | fique fiber | elastic modulus | REINFORCEMENT | BIOCOMPOSITES
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 01/2015, Volume 112, pp. 129 - 146
The initial–boundary value problem for some nonlinear higher-order viscoelastic wave equation with a nonlinear source term in a bounded domain is studied. The... 
Nonlinear higher-order viscoelastic wave equation | Global existence | Lifespan estimate | Nonlinear source term | Blow-up | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | NONEXISTENCE | DECAY | HYPERBOLIC-EQUATIONS | Viscoelasticity | Boundary value problems | Mathematical analysis | Wave equations | Nonlinearity | Initial value problems | Energy of solution | Galerkin methods
Journal Article
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