Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 228, Issue 2, pp. 377 - 411

.... We prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition...

Compressible Navier–Stokes equations | Viscous polytropic fluids | Vacuum | Compressible Navier-Stokes equations | INCOMPRESSIBLE FLUIDS | GLOBAL EXISTENCE | compressible Navier-Stokes equations | BOUNDARY-VALUE-PROBLEMS | DENSITY | MATHEMATICS | NAVIER-STOKES EQUATIONS | COMPRESSIBLE FLUIDS | vacuum | HEAT-CONDUCTIVE GASES | UNIQUE SOLVABILITY | CRITICAL SPACES | viscous polytropic fluids | WEAK SOLUTIONS

Compressible Navier–Stokes equations | Viscous polytropic fluids | Vacuum | Compressible Navier-Stokes equations | INCOMPRESSIBLE FLUIDS | GLOBAL EXISTENCE | compressible Navier-Stokes equations | BOUNDARY-VALUE-PROBLEMS | DENSITY | MATHEMATICS | NAVIER-STOKES EQUATIONS | COMPRESSIBLE FLUIDS | vacuum | HEAT-CONDUCTIVE GASES | UNIQUE SOLVABILITY | CRITICAL SPACES | viscous polytropic fluids | WEAK SOLUTIONS

Journal Article

ADVANCES IN DIFFERENCE EQUATIONS, ISSN 1687-1847, 06/2017, Volume 2017, Issue 1, pp. 1 - 13

...) are given sequences of numbers. We give some sufficient conditions for the existence of a unique bounded solution to the difference equation and present an elegant proof based on a combination of theory of linear difference...

SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | unique bounded solutions | linear first-order difference equation | second-order difference equation | fixed point theorem | Fixed point theory | Theorems (Mathematics) | Usage | Difference equations | Sequences | Mathematical analysis | Theorem proving | Convergence

SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | unique bounded solutions | linear first-order difference equation | second-order difference equation | fixed point theorem | Fixed point theory | Theorems (Mathematics) | Usage | Difference equations | Sequences | Mathematical analysis | Theorem proving | Convergence

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 01/2016, Volume 612, pp. 102 - 125

Unique decomposition has been a subject of interest in process algebra for a long time (for example in BPP [1] or CCS [2,3]), as it provides a normal form and...

Weak bisimilarity | Unique decomposition | Word problem | Decidability | Normal form | Strong bisimilarity | Cancellation | Behavioral equivalence | Applied π-calculus | Equational theory | Process calculus | Cryptography and Security | Computer Science

Weak bisimilarity | Unique decomposition | Word problem | Decidability | Normal form | Strong bisimilarity | Cancellation | Behavioral equivalence | Applied π-calculus | Equational theory | Process calculus | Cryptography and Security | Computer Science

Journal Article

Journal of Computational Electronics, ISSN 1569-8025, 9/2015, Volume 14, Issue 3, pp. 773 - 787

... equation would simplify the practical use, but mean value theorem based results are sufficient to prove existence of bounded discrete steady state solutions...

Generalized Einstein relation | 65N12 | Dissipativity | 65N08 | Theoretical, Mathematical and Computational Physics | Optical and Electronic Materials | Degenerate semiconductors | Generalized Scharfetter–Gummel scheme | 35J55 | Engineering | Appl.Mathematics/Computational Methods of Engineering | Unique thermodynamic equilibrium | Bounded discrete steady state solutions | Mechanical Engineering | Fermi–Dirac statistics | Electrical Engineering | PHYSICS, APPLIED | SEMICONDUCTOR | Generalized Scharfetter-Gummel scheme | EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | DISCRETIZATION | Fermi-Dirac statistics | DIFFUSION SYSTEMS | Stability | Approximation | Discretization | Semiconductors | Mathematical analysis | Chemical potential | Mathematical models | Steady state

Generalized Einstein relation | 65N12 | Dissipativity | 65N08 | Theoretical, Mathematical and Computational Physics | Optical and Electronic Materials | Degenerate semiconductors | Generalized Scharfetter–Gummel scheme | 35J55 | Engineering | Appl.Mathematics/Computational Methods of Engineering | Unique thermodynamic equilibrium | Bounded discrete steady state solutions | Mechanical Engineering | Fermi–Dirac statistics | Electrical Engineering | PHYSICS, APPLIED | SEMICONDUCTOR | Generalized Scharfetter-Gummel scheme | EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | DISCRETIZATION | Fermi-Dirac statistics | DIFFUSION SYSTEMS | Stability | Approximation | Discretization | Semiconductors | Mathematical analysis | Chemical potential | Mathematical models | Steady state

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 340, Issue 2, pp. 1226 - 1234

Given a strictly convex, smooth, and bounded domain Ω in R n we establish the existence of a negative convex solution in C ∞ ( Ω ) ∩ C ( Ω...

Singular boundary value problem | Monge–Ampère equation | Monge-Ampère equation | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | singular boundary value problem | Monge-Ampere equation | UNIQUE SOLUTION | NONLINEARITY | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | CONVECTION TERM | ASYMPTOTIC-BEHAVIOR

Singular boundary value problem | Monge–Ampère equation | Monge-Ampère equation | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | singular boundary value problem | Monge-Ampere equation | UNIQUE SOLUTION | NONLINEARITY | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | CONVECTION TERM | ASYMPTOTIC-BEHAVIOR

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2015, Volume 280, Issue 3, pp. 707 - 732

...Math. Z. (2015) 280:707–732 DOI 10.1007/s00209-015-1444-5 Mathematische Zeitschrift Existence, unique continuation and symmetry of least energy nodal solutions...

Nodal solutions | 35B06 | Foliated Schwarz symmetry | 35B05 | Primary 35J25 | Unique continuation | Sublinear Neumann problem | Mathematics, general | Mathematics | 35J15 | Secondary 35J20 | MATHEMATICS | DIFFERENTIAL-EQUATIONS | Analysis of PDEs

Nodal solutions | 35B06 | Foliated Schwarz symmetry | 35B05 | Primary 35J25 | Unique continuation | Sublinear Neumann problem | Mathematics, general | Mathematics | 35J15 | Secondary 35J20 | MATHEMATICS | DIFFERENTIAL-EQUATIONS | Analysis of PDEs

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 08/2015, Volume 2015, Issue 216, pp. 1 - 28

.... The purpose of this paper is to prove the existence of a unique, classical solution to this system of equations under periodic boundary conditions.

Fiuid | Existence | Uniqueness | Compressible | MATHEMATICS | MATHEMATICS, APPLIED | UNIQUE SOLUTION | compressible | uniqueness | ELLIPTIC EQUATION | fluid

Fiuid | Existence | Uniqueness | Compressible | MATHEMATICS | MATHEMATICS, APPLIED | UNIQUE SOLUTION | compressible | uniqueness | ELLIPTIC EQUATION | fluid

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 3/2011, Volume 23, Issue 1, pp. 1 - 44

...J Dyn Diff Equat (2011) 23:1–44 DOI 10.1007/s10884-010-9200-3 Existence, Uniqueness, and Stability of Generalized Traveling Waves in Time Dependent Monostable...

Generalized traveling wave solution | Almost periodic function | 35B15 | 35B35 | Wave speed | Mathematics | 35K57 | Super-solution | 35K55 | Monostable equation | Ordinary Differential Equations | Average propagating speed | 92D25 | Sub-solution | Wave profile | Unique ergodic function | Applications of Mathematics | 35B40 | Spreading speed | Partial Differential Equations | Generalized traveling wave solution wave speed | Sub-solution unique ergodic function | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | DIFFUSION EQUATIONS | MATHEMATICS | ASYMPTOTIC SPEEDS | KPP MODELS | PROPAGATING SPEEDS | DYNAMICS | CONVERGENCE | SYSTEMS | FRONT SPEED-UP | SPREADING SPEEDS

Generalized traveling wave solution | Almost periodic function | 35B15 | 35B35 | Wave speed | Mathematics | 35K57 | Super-solution | 35K55 | Monostable equation | Ordinary Differential Equations | Average propagating speed | 92D25 | Sub-solution | Wave profile | Unique ergodic function | Applications of Mathematics | 35B40 | Spreading speed | Partial Differential Equations | Generalized traveling wave solution wave speed | Sub-solution unique ergodic function | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | DIFFUSION EQUATIONS | MATHEMATICS | ASYMPTOTIC SPEEDS | KPP MODELS | PROPAGATING SPEEDS | DYNAMICS | CONVERGENCE | SYSTEMS | FRONT SPEED-UP | SPREADING SPEEDS

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 06/2012, Volume 55, Issue 2, pp. 285 - 296

For the $n$ -th order nonlinear differential equation, ${{y}^{(n)}}\,=\,f(x,\,y,\,y\prime ,\ldots ,\,{{y}^{(n-1)}})$ , we consider uniqueness implies uniqueness and existence results for solutions satisfying certain...

Boundary value problem | Unique solvability | Existence | Nonlinear interpolation | Uniqueness | MATHEMATICS | uniqueness | existence | boundary value problem | TIME-SCALE | nonlinear interpolation | unique solvability

Boundary value problem | Unique solvability | Existence | Nonlinear interpolation | Uniqueness | MATHEMATICS | uniqueness | existence | boundary value problem | TIME-SCALE | nonlinear interpolation | unique solvability

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 388, Issue 1, pp. 627 - 644

.... The existence of a weak solution to stationary problem is proved too, and a condition guaranteeing the uniqueness of solution is also given.

Sphere | Incompressible fluid dynamics | Unique solvability | MATHEMATICS, APPLIED | 2-DIMENSIONAL NAVIER-STOKES | INSTABILITY | APPROXIMATION | STABILITY | EQUATIONS | HYDRODYNAMICS | POLYNOMIALS | MATHEMATICS | WAVE | FLOWS | GLOBAL-SOLUTIONS | Fluid dynamics | Projectors

Sphere | Incompressible fluid dynamics | Unique solvability | MATHEMATICS, APPLIED | 2-DIMENSIONAL NAVIER-STOKES | INSTABILITY | APPROXIMATION | STABILITY | EQUATIONS | HYDRODYNAMICS | POLYNOMIALS | MATHEMATICS | WAVE | FLOWS | GLOBAL-SOLUTIONS | Fluid dynamics | Projectors

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 10/2019, Volume 127, pp. 422 - 427

.... In this paper we are established the existence of positive solutions (EPS) and the Hyers-Ulam (HU...

ABC-fractional differential equation | p-Laplacian operator | Unique solution | Green’s function | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | POSITIVE SOLUTIONS | Green's function | 1ST-ORDER | PHYSICS, MATHEMATICAL | FRAME

ABC-fractional differential equation | p-Laplacian operator | Unique solution | Green’s function | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | POSITIVE SOLUTIONS | Green's function | 1ST-ORDER | PHYSICS, MATHEMATICAL | FRAME

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2012, Volume 61, Issue 1, pp. 15 - 30

We study via Carleman estimates the sharpest possible exponential decay for waveguide solutions to the Laplace equation $({\partial...

Waveguides | Mathematical theorems | Infinity | Commutators | Unique continuation | Carleman estimates | INFINITY | MATHEMATICS | waveguides | unique continuation | SCHRODINGER EVOLUTIONS | EQUATIONS

Waveguides | Mathematical theorems | Infinity | Commutators | Unique continuation | Carleman estimates | INFINITY | MATHEMATICS | waveguides | unique continuation | SCHRODINGER EVOLUTIONS | EQUATIONS

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2016, Volume 13, Issue 5, pp. 2339 - 2351

A general approach is presented for proving existence of multiple solutions of the third-order nonlinear differential equation $$Au^{\prime\prime\prime}(x) + u...

special function | 34B15 | 35G30 | 35G60 | Mathematics, general | Closed-form solution | Mathematics | multiple solutions | exact analytical solution | unique solution | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | HOMOTOPY-PERTURBATION METHOD | Differential equations

special function | 34B15 | 35G30 | 35G60 | Mathematics, general | Closed-form solution | Mathematics | multiple solutions | exact analytical solution | unique solution | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | HOMOTOPY-PERTURBATION METHOD | Differential equations

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2013, Volume 64, Issue 1, pp. 83 - 100

.... In particular, using the Schauder fixed point theorem, we are able to establish existence of solutions...

Engineering | Navier–Stokes equations | Mathematical Methods in Physics | 34B15 | Rotating flow | Magneto-hydrodynamic flow | Existence theorem | Schauder fixed point theorem | Nonlinear system | 35A01 | Theoretical and Applied Mechanics | Navier-Stokes equations | MATHEMATICS, APPLIED | ROTATIONALLY SYMMETRIC FLOW | EQUATIONS | LAMINAR BOUNDARY-LAYER | STEADY FLOW | VERTICAL PLANE | NON-UNIQUE SOLUTIONS | SWIRLING FLOW | ASYMMETRIC FLOW | VISCOUS-FLUID | DISK | Electric generators | Rotating spheres | Nonlinear dynamics | Magnetohydrodynamics | Approximation | MHD | Mathematical models | Rotating | Dynamical systems

Engineering | Navier–Stokes equations | Mathematical Methods in Physics | 34B15 | Rotating flow | Magneto-hydrodynamic flow | Existence theorem | Schauder fixed point theorem | Nonlinear system | 35A01 | Theoretical and Applied Mechanics | Navier-Stokes equations | MATHEMATICS, APPLIED | ROTATIONALLY SYMMETRIC FLOW | EQUATIONS | LAMINAR BOUNDARY-LAYER | STEADY FLOW | VERTICAL PLANE | NON-UNIQUE SOLUTIONS | SWIRLING FLOW | ASYMMETRIC FLOW | VISCOUS-FLUID | DISK | Electric generators | Rotating spheres | Nonlinear dynamics | Magnetohydrodynamics | Approximation | MHD | Mathematical models | Rotating | Dynamical systems

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 10/2019, Volume 64, Issue 10, pp. 4245 - 4251

This paper investigates the existence of nonimpulsive unique solution and stochastic stability problems for the discrete-time linear rectangular descriptor Markov jump systems at two cases...

Discrete-time Markov jump systems (MJS) | Symmetric matrices | rectangular descriptor systems | Markov processes | Power system stability | Controllability | Stability analysis | Mathematical model | unique solution | stability analysis | STABILIZATION | OBSERVABILITY | OBSERVER DESIGN | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Discrete-time Markov jump systems (MJS) | Symmetric matrices | rectangular descriptor systems | Markov processes | Power system stability | Controllability | Stability analysis | Mathematical model | unique solution | stability analysis | STABILIZATION | OBSERVABILITY | OBSERVER DESIGN | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2008, Volume 45, Issue 3, pp. 645 - 681

.... We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition...

Vacuum | Heat-conducting incompressible Navier-Stokes equations | Strong solutions | DENSITY | MATHEMATICS | MATHEMATICS, APPLIED | EXTERIOR DOMAINS | NAVIER-STOKES EQUATIONS | vacuum | BOUNDARY-VALUE PROBLEM | REGULARITY | UNIQUE SOLVABILITY | strong solutions | heat-conducting incompressible Navier-Stokes equations

Vacuum | Heat-conducting incompressible Navier-Stokes equations | Strong solutions | DENSITY | MATHEMATICS | MATHEMATICS, APPLIED | EXTERIOR DOMAINS | NAVIER-STOKES EQUATIONS | vacuum | BOUNDARY-VALUE PROBLEM | REGULARITY | UNIQUE SOLVABILITY | strong solutions | heat-conducting incompressible Navier-Stokes equations

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2009, Volume 137, Issue 8, pp. 2697 - 2707

In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem...

Datasets | Interpolation | Sufficient conditions | Mathematical theorems | Terminology | Hilbert spaces | Mathematical vectors | Mathematical functions | Operator theory | Linear fractional maps | Unique solution | Commutant lifting | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | NORM | linear fractional maps | unique solution

Datasets | Interpolation | Sufficient conditions | Mathematical theorems | Terminology | Hilbert spaces | Mathematical vectors | Mathematical functions | Operator theory | Linear fractional maps | Unique solution | Commutant lifting | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | NORM | linear fractional maps | unique solution

Journal Article

Nagoya mathematical journal, ISSN 0027-7630, 09/2010, Volume 199, pp. 1 - 14

Suppose that [μ] T(Δ) is a point of the universal Teichmüller space T(Δ). In 1998, Božin, Lakic, Marković, and Mateljević showed that there exists μ such that...

MATHEMATICS | QUASI-CONFORMAL MAPPINGS | UNIQUE EXTREMALITY | SETS | 30C75 | 30C62

MATHEMATICS | QUASI-CONFORMAL MAPPINGS | UNIQUE EXTREMALITY | SETS | 30C75 | 30C62

Journal Article

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2014, Volume 46, Issue 6, pp. 3891 - 3912

.... An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown...

variational-hemivariational inequality | MATHEMATICS, APPLIED | Clarke subdifferential | MECHANICS | finite element solution | convergence | existence and unique-ness | UNILATERAL PROBLEMS | continuous dependence | error estimates | frictional contact | Mathematics

variational-hemivariational inequality | MATHEMATICS, APPLIED | Clarke subdifferential | MECHANICS | finite element solution | convergence | existence and unique-ness | UNILATERAL PROBLEMS | continuous dependence | error estimates | frictional contact | Mathematics

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2019, Volume 42, Issue 18, pp. 7482 - 7493

.... We introduce a nonlinear Gauss‐Seidel fixed point scheme which allows to obtain a constructive proof of the existence and the uniqueness, when a small nonzero source term is considered...

finite elements approximation | buckling phenomena | Föppl‐von Kàrmàn equations | unique weak solution | MATHEMATICS, APPLIED | Foppl-von Karman equations | Computer simulation | Thin plates | Uniqueness

finite elements approximation | buckling phenomena | Föppl‐von Kàrmàn equations | unique weak solution | MATHEMATICS, APPLIED | Foppl-von Karman equations | Computer simulation | Thin plates | Uniqueness

Journal Article

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