2013, Fifth edition., ISBN 9780321797056, xix, 756 pages

This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations...

Differential equations, Partial | Fourier series | Boundary value problems

Differential equations, Partial | Fourier series | Boundary value problems

Book

1993, 1, ISBN 0849386365, 285

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse...

Mathematical models | Differential equations | Differential Equations | Differential equations-Mathematical models

Mathematical models | Differential equations | Differential Equations | Differential equations-Mathematical models

Book

1994, ISBN 9780849394065, x, 227

This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon...

Harmonic functions | Conformal mapping | Applied Mathematics | Differential Equations

Harmonic functions | Conformal mapping | Applied Mathematics | Differential Equations

Book

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3, p. 1

We consider a nonlinear Dirichlet elliptic problem driven by the sum of a p-Laplacian and a Laplacian [a (p, 2)-equation...

MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | NODAL SOLUTIONS | P-LAPLACE EQUATIONS | NONTRIVIAL SOLUTIONS | ELLIPTIC-EQUATIONS | Q)-EQUATIONS | Computer science

MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | NODAL SOLUTIONS | P-LAPLACE EQUATIONS | NONTRIVIAL SOLUTIONS | ELLIPTIC-EQUATIONS | Q)-EQUATIONS | Computer science

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2011, Volume 61, Issue 8, pp. 1963 - 1967

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations...

Laplace transform method | Homotopy perturbation method | Nonlinear advection equations | He’s polynomials | He's polynomials | VARIATIONAL ITERATION METHOD | MATHEMATICS, APPLIED | Analysis | Methods | Algorithms

Laplace transform method | Homotopy perturbation method | Nonlinear advection equations | He’s polynomials | He's polynomials | VARIATIONAL ITERATION METHOD | MATHEMATICS, APPLIED | Analysis | Methods | Algorithms

Journal Article

Probability theory and related fields, ISSN 1432-2064, 2018, Volume 173, Issue 3-4, pp. 1063 - 1098

...Probab. Theory Relat. Fields (2019) 173:1063–1098 https://doi.org/10.1007/s00440-018-0848-7 Regularization by noise for stochastic Hamilton–Jacobi equations...

Stochastic p -Laplace equation | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Stochastic total variation flow | Mathematics | Reflected SDE | Quantitative Finance | Stochastic Hamilton–Jacobi equations | 35L65 | regularization by noise | Operations Research/Decision Theory | 60H15 | 65M12 | Stochastic p-Laplace equation | Stochastic Hamilton–Jacobi equations; regularization by noise | STATISTICS & PROBABILITY | Stochastic Hamilton-Jacobi equations | Regularization | Probability

Stochastic p -Laplace equation | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Stochastic total variation flow | Mathematics | Reflected SDE | Quantitative Finance | Stochastic Hamilton–Jacobi equations | 35L65 | regularization by noise | Operations Research/Decision Theory | 60H15 | 65M12 | Stochastic p-Laplace equation | Stochastic Hamilton–Jacobi equations; regularization by noise | STATISTICS & PROBABILITY | Stochastic Hamilton-Jacobi equations | Regularization | Probability

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 16

...Wu and Baleanu Advances in Diﬀerence Equations 2013, 2013:21 http://www.advancesindifferenceequations.com/content/2013/1/21 R E S E A R C H Open Access New...

fractional calculus | time scales | q -calculus | symbolic computation | Mathematics | variational iteration method | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Laplace transform | Partial Differential Equations | Variational iteration method | Q-calculus | Symbolic computation | Time scales | Fractional calculus | MATHEMATICS | MATHEMATICS, APPLIED | Q-INTEGRALS | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | DERIVATIVES | q-calculus | Linear systems | Usage | Difference equations | Innovations | Laplace transformation | Iterative methods (Mathematics) | Methods | Calculi | Mathematical analysis | Differential equations | Initial value problems | Calculus | Iterative methods | Concentrates

fractional calculus | time scales | q -calculus | symbolic computation | Mathematics | variational iteration method | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Laplace transform | Partial Differential Equations | Variational iteration method | Q-calculus | Symbolic computation | Time scales | Fractional calculus | MATHEMATICS | MATHEMATICS, APPLIED | Q-INTEGRALS | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | DERIVATIVES | q-calculus | Linear systems | Usage | Difference equations | Innovations | Laplace transformation | Iterative methods (Mathematics) | Methods | Calculi | Mathematical analysis | Differential equations | Initial value problems | Calculus | Iterative methods | Concentrates

Journal Article

Journal of Physics: Condensed Matter, ISSN 0953-8984, 03/2010, Volume 22, Issue 8, pp. 085005 - 085005

... (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented...

ELASTICITY | PHYSICS, CONDENSED MATTER | EQUILIBRIUM | SOLIDS | THIN-PLATE | CAPILLARITY | RIDGE | Stresses | Thermodynamics | Deformation | Condensed matter | Mathematical analysis | Laplace equation | Formability | Contact

ELASTICITY | PHYSICS, CONDENSED MATTER | EQUILIBRIUM | SOLIDS | THIN-PLATE | CAPILLARITY | RIDGE | Stresses | Thermodynamics | Deformation | Condensed matter | Mathematical analysis | Laplace equation | Formability | Contact

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2011, Volume 74, Issue 18, pp. 7543 - 7561

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on a Banach space with locally monotone operators, which is a generalization of the classical...

Porous medium equation | [formula omitted]-Laplace equation | Pseudo-monotone | Reaction–diffusion equation | Navier–Stokes equation | Locally monotone | Nonlinear evolution equation | Burgers equation | Reactiondiffusion equation | p-Laplace equation | NavierStokes equation | MATHEMATICS, APPLIED | FAST-DIFFUSION-EQUATIONS | SPACES | ATTRACTOR | MODEL | Navier-Stokes equation | MATHEMATICS | Reaction-diffusion equation | GENERALIZED POROUS-MEDIA | HARNACK INEQUALITY | NON-LINEAR EQUATIONS | Operators | Mathematical analysis | Uniqueness | Nonlinear evolution equations | Mathematical models | Three dimensional | Navier-Stokes equations

Porous medium equation | [formula omitted]-Laplace equation | Pseudo-monotone | Reaction–diffusion equation | Navier–Stokes equation | Locally monotone | Nonlinear evolution equation | Burgers equation | Reactiondiffusion equation | p-Laplace equation | NavierStokes equation | MATHEMATICS, APPLIED | FAST-DIFFUSION-EQUATIONS | SPACES | ATTRACTOR | MODEL | Navier-Stokes equation | MATHEMATICS | Reaction-diffusion equation | GENERALIZED POROUS-MEDIA | HARNACK INEQUALITY | NON-LINEAR EQUATIONS | Operators | Mathematical analysis | Uniqueness | Nonlinear evolution equations | Mathematical models | Three dimensional | Navier-Stokes equations

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2017, Volume 91, Issue 1, pp. 307 - 317

...) equation of fractional order. The F–N equation describes the transmission of nerve impulses...

Fractional reduced differential transform scheme | Engineering | Vibration, Dynamical Systems, Control | Transmission of nerve impulses | Fractional Fitzhugh–Nagumo equation | Classical Mechanics | Homotopy polynomials | q -Homotopy analysis transform method | Automotive Engineering | Mechanical Engineering | q-Homotopy analysis transform method | ORDER | MECHANICS | MODELS | TRANSFORM METHOD | EXAMPLE | Fractional Fitzhugh-Nagumo equation | HOMOTOPY ANALYSIS METHOD | ENGINEERING, MECHANICAL | Analysis | Algorithms | Impulses | Error analysis | Numerical analysis | Differential equations | Differential thermal analysis | Polynomials | Laplace transforms

Fractional reduced differential transform scheme | Engineering | Vibration, Dynamical Systems, Control | Transmission of nerve impulses | Fractional Fitzhugh–Nagumo equation | Classical Mechanics | Homotopy polynomials | q -Homotopy analysis transform method | Automotive Engineering | Mechanical Engineering | q-Homotopy analysis transform method | ORDER | MECHANICS | MODELS | TRANSFORM METHOD | EXAMPLE | Fractional Fitzhugh-Nagumo equation | HOMOTOPY ANALYSIS METHOD | ENGINEERING, MECHANICAL | Analysis | Algorithms | Impulses | Error analysis | Numerical analysis | Differential equations | Differential thermal analysis | Polynomials | Laplace transforms

Journal Article

2012, International series in mathematics, ISBN 0763772569, xvi, 316

Book

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2018, Volume 75, Issue 3, pp. 740 - 754

.... It is clear that in order to find conservation laws for a given partial differential equations (PDEs...

Laplace operator | Noether’s operator | Fractional symmetry | Fractional diffusion equation | Fractional conservation laws | Noether's operator | MATHEMATICS, APPLIED | Thermodynamics | Laws, regulations and rules | Environmental law | Quantum theory | Differential equations

Laplace operator | Noether’s operator | Fractional symmetry | Fractional diffusion equation | Fractional conservation laws | Noether's operator | MATHEMATICS, APPLIED | Thermodynamics | Laws, regulations and rules | Environmental law | Quantum theory | Differential equations

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 10/2016, Volume 60, pp. 56 - 60

In this paper, we study the nonexistence of solutions for p-Laplace equations with critical Sobolev...

[formula omitted]-Laplace equations | Pohozaev identity | Nonexistence | Sobolev–Hardy critical exponents | Sobolev-Hardy critical exponents | p-Laplace equations | MATHEMATICS, APPLIED | EXPONENTS | LINEAR ELLIPTIC-EQUATIONS

[formula omitted]-Laplace equations | Pohozaev identity | Nonexistence | Sobolev–Hardy critical exponents | Sobolev-Hardy critical exponents | p-Laplace equations | MATHEMATICS, APPLIED | EXPONENTS | LINEAR ELLIPTIC-EQUATIONS

Journal Article

Annali di matematica pura ed applicata, ISSN 1618-1891, 2019, Volume 198, Issue 5, pp. 1651 - 1673

We consider the Dirichlet problem for the nonhomogeneous equation $$-\Delta _p u -\Delta _q u = \alpha |u|^{p-2}u + \beta |u|^{q-2}u + f(x)$$ - Δ p u - Δ q u = α | u | p - 2 u + β | u | q - 2 u + f ( x ) in a bounded domain...

35J20 | Fredholm alternative | 35J62 | Positive solutions | Linking method | Mathematics, general | Maximum principle | Mathematics | 35P30 | 35B50 | ( p , q )-Laplacian | Existence of solutions | (p, q)-Laplacian | Mathematics - Analysis of PDEs

35J20 | Fredholm alternative | 35J62 | Positive solutions | Linking method | Mathematics, general | Maximum principle | Mathematics | 35P30 | 35B50 | ( p , q )-Laplacian | Existence of solutions | (p, q)-Laplacian | Mathematics - Analysis of PDEs

Journal Article

Neural computing & applications, ISSN 1433-3058, 2017, Volume 30, Issue 10, pp. 3063 - 3070

In this work, we concentrate on the analysis of the time-fractional Rosenau–Hyman equation occurring in the formation of patterns in liquid drops via q-homotopy analysis transform technique and reduced differential transform approach...

Computational Biology/Bioinformatics | q -Homotopy analysis transform technique | Artificial Intelligence | Reduced differential transform technique | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Time-fractional Rosenau–Hyman equation | Liquid drops | Laplace transform method | Computational Science and Engineering | Probability and Statistics in Computer Science | q-Homotopy analysis transform technique | PARTIAL-DIFFERENTIAL-EQUATIONS | ANALYSIS TRANSFORM METHOD | COMPACTONS | HOMOTOPY PERTURBATION METHOD | DERIVATIVES | Time-fractional Rosenau-Hyman equation | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Analysis | Algorithms

Computational Biology/Bioinformatics | q -Homotopy analysis transform technique | Artificial Intelligence | Reduced differential transform technique | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Time-fractional Rosenau–Hyman equation | Liquid drops | Laplace transform method | Computational Science and Engineering | Probability and Statistics in Computer Science | q-Homotopy analysis transform technique | PARTIAL-DIFFERENTIAL-EQUATIONS | ANALYSIS TRANSFORM METHOD | COMPACTONS | HOMOTOPY PERTURBATION METHOD | DERIVATIVES | Time-fractional Rosenau-Hyman equation | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Analysis | Algorithms

Journal Article

2006, 3rd ed., Schaum's outline series, ISBN 0071456872, xiv, 385

Book

18.
Full Text
Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation

Journal of scientific computing, ISSN 1573-7691, 2016, Volume 71, Issue 2, pp. 469 - 498

In this paper, we examine the Cauchy problem of the Laplace equation. Motivated by the incompleteness of the single-layer potential function method, we investigate the double-layer potential function method...

65R32 | Computational Mathematics and Numerical Analysis | Algorithms | 31A25 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | 65N21 | Boundary element method | Morozov discrepancy principle | Cauchy problem | MATHEMATICS, APPLIED | LINEAR ELASTICITY | ALGORITHM | NUMERICAL EXPERIMENTS | POTENTIAL PROBLEMS | FORMULATION | ELLIPTIC-OPERATORS | ELEMENT SOLUTION | KERNEL | REGULARIZATION | DEGENERATE SCALE | Signal processing | Analysis | Methods

65R32 | Computational Mathematics and Numerical Analysis | Algorithms | 31A25 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | 65N21 | Boundary element method | Morozov discrepancy principle | Cauchy problem | MATHEMATICS, APPLIED | LINEAR ELASTICITY | ALGORITHM | NUMERICAL EXPERIMENTS | POTENTIAL PROBLEMS | FORMULATION | ELLIPTIC-OPERATORS | ELEMENT SOLUTION | KERNEL | REGULARIZATION | DEGENERATE SCALE | Signal processing | Analysis | Methods

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/2016, Volume 347, Issue 3, pp. 875 - 901

In this paper we study radial solutions for the following equation $$\Delta u(x)+f (u(x), |x|) = 0,$$ Δ u ( x ) + f ( u ( x ) , | x | ) = 0 , where $${x...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | EXISTENCE | POSITIVE RADIAL SOLUTIONS | SEMILINEAR ELLIPTIC-EQUATIONS | CRITICAL EXPONENT | R(N) | SINGULAR GROUND-STATES | DELTA-U+K(VERTICAL-BAR-X-VERTICAL-BAR) U(P)=0 | PHYSICS, MATHEMATICAL

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | EXISTENCE | POSITIVE RADIAL SOLUTIONS | SEMILINEAR ELLIPTIC-EQUATIONS | CRITICAL EXPONENT | R(N) | SINGULAR GROUND-STATES | DELTA-U+K(VERTICAL-BAR-X-VERTICAL-BAR) U(P)=0 | PHYSICS, MATHEMATICAL

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2018, Volume 194, p. 111391

We study the possibility of prescribing infinite initial values for solutions of the Evolutionary p-Laplace Equation in the fast diffusion case p>2...

Friendly giant | Parabolic [formula omitted]-Laplace equation | Parabolic p-Laplace equation | MATHEMATICS | MATHEMATICS, APPLIED | DEGENERATE

Friendly giant | Parabolic [formula omitted]-Laplace equation | Parabolic p-Laplace equation | MATHEMATICS | MATHEMATICS, APPLIED | DEGENERATE

Journal Article