Computers & mathematics with applications (1987), ISSN 0898-1221, 2017, Volume 73, Issue 6, pp. 1016 - 1027

...), which can be used to simulate anomalous diffusion in fractal media. We firstly give the concept of the weak solutions and establish the existence criterion of weak solutions by means of Galerkin approximations in the case that the dimension n≤4...

Navier–Stokes equations | Weak solutions | Optimal controls | Caputo fractional derivative | Existence | MATHEMATICS, APPLIED | Navier-Stokes equations | Fluid dynamics

Navier–Stokes equations | Weak solutions | Optimal controls | Caputo fractional derivative | Existence | MATHEMATICS, APPLIED | Navier-Stokes equations | Fluid dynamics

Journal Article

Archive for rational mechanics and analysis, ISSN 1432-0673, 2006, Volume 183, Issue 2, pp. 215 - 239

... is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation...

Mechanics | Fluids | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | Complexity | BREAKING | MULTIPEAKONS | WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | WEAK SOLUTIONS | SHALLOW-WATER EQUATION | PEAKONS | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Mechanics | Fluids | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | Complexity | BREAKING | MULTIPEAKONS | WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | WEAK SOLUTIONS | SHALLOW-WATER EQUATION | PEAKONS | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Angewandte Chemie (International ed.), ISSN 1433-7851, 2015, Volume 54, Issue 38, pp. 11093 - 11096

The A‐site mixed‐ammonium solid solutions of metal–organic perovskites [(NH2NH3)x(CH3NH3)1−x][Mn(HCOO)3] (x=1.00–0.67) exhibit para‐ to ferroelectric diffuse phase transitions with lowered transition temperatures from x...

phase transitions | manganese | dielectric properties | metal–organic perovskites | DESIGN | WEAK FERROMAGNETISM | THERMAL-EXPANSION | METAL-ORGANIC FRAMEWORK | FERROELECTRICITY | metal-organic perovskites | CHEMISTRY, MULTIDISCIPLINARY | PROMINENT DIELECTRIC ANOMALIES | ORDER | FORMATE FRAMEWORK | PHASE-TRANSITION | MULTIFERROICS | Solid solutions | Phase transitions | Dielectric constant | Transition temperature | Ferroelectricity | Ferroelectric materials | Phase transformations | Distortion | Perovskites | Permittivity

phase transitions | manganese | dielectric properties | metal–organic perovskites | DESIGN | WEAK FERROMAGNETISM | THERMAL-EXPANSION | METAL-ORGANIC FRAMEWORK | FERROELECTRICITY | metal-organic perovskites | CHEMISTRY, MULTIDISCIPLINARY | PROMINENT DIELECTRIC ANOMALIES | ORDER | FORMATE FRAMEWORK | PHASE-TRANSITION | MULTIFERROICS | Solid solutions | Phase transitions | Dielectric constant | Transition temperature | Ferroelectricity | Ferroelectric materials | Phase transformations | Distortion | Perovskites | Permittivity

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2018, Volume 376-377, pp. 259 - 265

We prove a version of Onsager’s conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. (2017...

Statistical solutions | Onsager’s conjecture | Energy conservation | Incompressible Euler equations | Onsager's conjecture | DISSIPATION | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MEASURE-VALUED SOLUTIONS | ENERGY-CONSERVATION | LAWS | NAVIER-STOKES EQUATIONS | WEAK SOLUTIONS | EULER EQUATIONS

Statistical solutions | Onsager’s conjecture | Energy conservation | Incompressible Euler equations | Onsager's conjecture | DISSIPATION | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MEASURE-VALUED SOLUTIONS | ENERGY-CONSERVATION | LAWS | NAVIER-STOKES EQUATIONS | WEAK SOLUTIONS | EULER EQUATIONS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 11/2017, Volume 163, pp. 177 - 200

This paper concerns the global stability of weak solutions for the multilayer system introduced by Audusse et al...

Navier–Stokes equations | Free surface flow | Degenerate viscosities | Global weak solutions | Saint–Venant model | DERIVATION | EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | FORM | Saint-Venant model | NUMERICAL VALIDATION | SHALLOW-WATER MODEL | MATHEMATICS | SCHEME | BOUSSINESQ EQUATIONS | Navier-Stokes equations | WAVE-PROPAGATION | Modeling and Simulation | Mathematics | Analysis of PDEs | Computer Science

Navier–Stokes equations | Free surface flow | Degenerate viscosities | Global weak solutions | Saint–Venant model | DERIVATION | EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | FORM | Saint-Venant model | NUMERICAL VALIDATION | SHALLOW-WATER MODEL | MATHEMATICS | SCHEME | BOUSSINESQ EQUATIONS | Navier-Stokes equations | WAVE-PROPAGATION | Modeling and Simulation | Mathematics | Analysis of PDEs | Computer Science

Journal Article

ANALYSIS AND APPLICATIONS, ISSN 0219-5305, 01/2007, Volume 5, Issue 1, pp. 1 - 27

This paper is devoted to the continuation of solutions to the Camassa-Holm equation after wave breaking...

MATHEMATICS | BREAKING | MATHEMATICS, APPLIED | conservation law | BANACH-SPACES | WAVE-EQUATION | dissipative solutions | non-local source | WEAK SOLUTIONS | Camassa-Holm equation | SHALLOW-WATER EQUATION | CONSERVATIVE SOLUTIONS

MATHEMATICS | BREAKING | MATHEMATICS, APPLIED | conservation law | BANACH-SPACES | WAVE-EQUATION | dissipative solutions | non-local source | WEAK SOLUTIONS | Camassa-Holm equation | SHALLOW-WATER EQUATION | CONSERVATIVE SOLUTIONS

Journal Article

Communications on pure and applied mathematics, ISSN 0010-3640, 2012, Volume 65, Issue 4, pp. 549 - 585

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier...

SPACE | MATHEMATICS | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | BEHAVIOR | VISCOUS FLUIDS | BLOW-UP | WEAK SOLUTIONS | FLOW | DISCONTINUOUS INITIAL DATA | UNIQUENESS

SPACE | MATHEMATICS | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | BEHAVIOR | VISCOUS FLUIDS | BLOW-UP | WEAK SOLUTIONS | FLOW | DISCONTINUOUS INITIAL DATA | UNIQUENESS

Journal Article

The European Physical Journal C, ISSN 1434-6044, 9/2015, Volume 75, Issue 9, pp. 1 - 8

We find some new exact cosmological solutions for the covariant scalar–tensor–vector gravity theory, the so-called modified gravity (MOG...

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | SYMMETRIES | WEAK-FIELD APPROXIMATION | OBSERVATIONAL TEST | DYNAMICS | MODEL | NOETHER | SCALAR | MODIFIED GRAVITY | PHYSICS, PARTICLES & FIELDS | Gravitation | Mathematical analysis | Exact solutions | Generators | Fields (mathematics) | Vectors (mathematics) | Symmetry | Physics and Astronomy (miscellaneous) | General Relativity and Quantum Cosmology | Engineering (miscellaneous) | Astrophysics - Astrophysics of Galaxies

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | SYMMETRIES | WEAK-FIELD APPROXIMATION | OBSERVATIONAL TEST | DYNAMICS | MODEL | NOETHER | SCALAR | MODIFIED GRAVITY | PHYSICS, PARTICLES & FIELDS | Gravitation | Mathematical analysis | Exact solutions | Generators | Fields (mathematics) | Vectors (mathematics) | Symmetry | Physics and Astronomy (miscellaneous) | General Relativity and Quantum Cosmology | Engineering (miscellaneous) | Astrophysics - Astrophysics of Galaxies

Journal Article

Social choice and welfare, ISSN 1432-217X, 2018, Volume 51, Issue 2, pp. 193 - 222

...Soc Choice Welf (2018) 51:193–222 https://doi.org/10.1007/s00355-018-1112-x ORIGINAL PAPER Extending tournament solutions Felix Brandt 1 · Markus Brill 2...

Economics | International Political Economy | Game Theory, Economics, Social and Behav. Sciences | Social Policy | Public Finance | Economic Theory/Quantitative Economics/Mathematical Methods | SHAPLEYS SADDLES | SET | CHOICE CORRESPONDENCES | GAMES | WEAK TOURNAMENTS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | WINNERS | Computer science | Social choice | Tournaments | Generalizations | Tournaments & championships | Property | Profiles

Economics | International Political Economy | Game Theory, Economics, Social and Behav. Sciences | Social Policy | Public Finance | Economic Theory/Quantitative Economics/Mathematical Methods | SHAPLEYS SADDLES | SET | CHOICE CORRESPONDENCES | GAMES | WEAK TOURNAMENTS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | WINNERS | Computer science | Social choice | Tournaments | Generalizations | Tournaments & championships | Property | Profiles

Journal Article

Calculus of variations and partial differential equations, ISSN 1432-0835, 2016, Volume 55, Issue 4, pp. 1 - 39

... of [2, 3), with smooth boundary. We show that it has global classical solutions if the initial data satisfy certain smallness conditions and give decay properties...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35B35 | Analysis | Theoretical, Mathematical and Computational Physics | 35Q35 | Mathematics | 92C17 | 35B40 | 35K55 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BACTERIA | PARABOLIC EQUATIONS | INITIAL-VALUE PROBLEM | BOUNDED DOMAINS | FLUID MODEL | NONLINEAR DIFFUSION | WEAK SOLUTIONS | KELLER-SEGEL MODELS | ASYMPTOTIC-BEHAVIOR

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35B35 | Analysis | Theoretical, Mathematical and Computational Physics | 35Q35 | Mathematics | 92C17 | 35B40 | 35K55 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BACTERIA | PARABOLIC EQUATIONS | INITIAL-VALUE PROBLEM | BOUNDED DOMAINS | FLUID MODEL | NONLINEAR DIFFUSION | WEAK SOLUTIONS | KELLER-SEGEL MODELS | ASYMPTOTIC-BEHAVIOR

Journal Article

11.
Full Text
Weak–strong uniqueness of solutions to entropy-dissipating reaction–diffusion equations

Nonlinear Analysis, ISSN 0362-546X, 08/2017, Volume 159, pp. 181 - 207

We establish a weak–strong uniqueness principle for solutions to entropy-dissipating reaction–diffusion equations...

Reaction–diffusion equation | Mass-action kinetics | Weak–strong uniqueness | RENORMALIZED SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSPORT | GLOBAL EXISTENCE | Weak-strong uniqueness | MASS | SYSTEMS | BLOWUP | Reaction diffusion equation

Reaction–diffusion equation | Mass-action kinetics | Weak–strong uniqueness | RENORMALIZED SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSPORT | GLOBAL EXISTENCE | Weak-strong uniqueness | MASS | SYSTEMS | BLOWUP | Reaction diffusion equation

Journal Article

Langmuir, ISSN 0743-7463, 10/2018, Volume 34, Issue 42, pp. 12653 - 12663

... poly(ionic liquid) (PIL) (P[VBTP][Cl]/P[VBuIm][Br]) segments show only lower critical solution temperature (LCST...

DIBLOCK COPOLYMERS | AQUEOUS-SOLUTIONS | BLOCK-COPOLYMERS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | POLY(N,N-DIMETHYLAMINOETHYL METHACRYLATE) | IONIC LIQUID | CHEMISTRY, MULTIDISCIPLINARY | PH-RESPONSIVE POLYMERS | N-ISOPROPYLACRYLAMIDE | THERMORESPONSIVE POLYMERS | WEAK POLYELECTROLYTES | BIOMEDICAL APPLICATIONS

DIBLOCK COPOLYMERS | AQUEOUS-SOLUTIONS | BLOCK-COPOLYMERS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | POLY(N,N-DIMETHYLAMINOETHYL METHACRYLATE) | IONIC LIQUID | CHEMISTRY, MULTIDISCIPLINARY | PH-RESPONSIVE POLYMERS | N-ISOPROPYLACRYLAMIDE | THERMORESPONSIVE POLYMERS | WEAK POLYELECTROLYTES | BIOMEDICAL APPLICATIONS

Journal Article

Nonlinearity, ISSN 1361-6544, 2010, Volume 23, Issue 5, pp. 1097 - 1107

.... Based on the method from Cao and Titi (2008 Indiana Univ. Math. J. 57 2643-61) we prove that the weak solution is regular, provided u(3...

CRITERIA | PRESSURE | MATHEMATICS, APPLIED | TERMS | DIRECTION | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Alignment | Infinity | Mathematical analysis | Fluid flow | Images | Nonlinearity | Criteria | Regularity

CRITERIA | PRESSURE | MATHEMATICS, APPLIED | TERMS | DIRECTION | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Alignment | Infinity | Mathematical analysis | Fluid flow | Images | Nonlinearity | Criteria | Regularity

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2019, Volume 343, pp. 166 - 185

In this work, the Bernstein–Bézier Finite Element Method (BBFEM) is implemented to solve short wave problems governed by the Helmholtz equation on unstructured...

Plane waves | Helmholtz equation | Finite elements | High frequency | Bernstein–Bézier | Wave problems | HELMHOLTZ PROBLEMS | H-P-VERSION | HIERARCHICAL ELEMENTS | SHAPE FUNCTIONS | PLANE-WAVES | WEAK VARIATIONAL FORMULATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | LOCAL MAPPINGS | UNITY METHOD | DISCONTINUOUS GALERKIN METHODS | Bernstein-Bezier | ULTRA-WEAK

Plane waves | Helmholtz equation | Finite elements | High frequency | Bernstein–Bézier | Wave problems | HELMHOLTZ PROBLEMS | H-P-VERSION | HIERARCHICAL ELEMENTS | SHAPE FUNCTIONS | PLANE-WAVES | WEAK VARIATIONAL FORMULATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | LOCAL MAPPINGS | UNITY METHOD | DISCONTINUOUS GALERKIN METHODS | Bernstein-Bezier | ULTRA-WEAK

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2019, Volume 77, Issue 5, pp. 1347 - 1357

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz...

Weak solution | Fractional differential equations | Fractional Laplacian | Faedo–Galerkin | Weak Caputo derivative | Landau–Lifshitz–Bloch equation | MATHEMATICS, APPLIED | Landau-Lifshitz-Bloch equation | BOUNDARY-VALUE-PROBLEMS | TIME | Faedo-Galerkin | Differential equations | Commutators | Galerkin method

Weak solution | Fractional differential equations | Fractional Laplacian | Faedo–Galerkin | Weak Caputo derivative | Landau–Lifshitz–Bloch equation | MATHEMATICS, APPLIED | Landau-Lifshitz-Bloch equation | BOUNDARY-VALUE-PROBLEMS | TIME | Faedo-Galerkin | Differential equations | Commutators | Galerkin method

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 10/2007, Volume 32, Issue 10, pp. 1511 - 1549

We show that the Camassa-Holm equation u t − u xxt + 3uu x − 2u x u xx − uu xxx = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u...

Secondary 35B10, 35Q53 | Primary 65M06, 65M12 | Conservative solutions | Camassa-Holm equation | MATHEMATICS | BREAKING | SCHEME | MATHEMATICS, APPLIED | GEOMETRIC APPROACH | WAVES | conservative solutions | ROD | WEAK SOLUTIONS | camassa-holm equation | SHALLOW-WATER EQUATION | PEAKONS

Secondary 35B10, 35Q53 | Primary 65M06, 65M12 | Conservative solutions | Camassa-Holm equation | MATHEMATICS | BREAKING | SCHEME | MATHEMATICS, APPLIED | GEOMETRIC APPROACH | WAVES | conservative solutions | ROD | WEAK SOLUTIONS | camassa-holm equation | SHALLOW-WATER EQUATION | PEAKONS

Journal Article