2007, OXFORD SCIENCE PUBLICATIONS. SER: OXFORD MATHEMATICAL MONOGRAPHS., ISBN 9780198569039, 647

The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the...

Boundary value problems | Mathematics | mathematical and statistical physics | Boundary layer theory | Nonlinear | Heat equation | Linear partial differential equations | Fluid flow | Mathematical biology | Lubrication | Diffusion | Heat transfer

Boundary value problems | Mathematics | mathematical and statistical physics | Boundary layer theory | Nonlinear | Heat equation | Linear partial differential equations | Fluid flow | Mathematical biology | Lubrication | Diffusion | Heat transfer

Book

2015, Mathematical surveys and monographs, ISBN 1470425580, Volume 207, xii, 479

Book

3.
Smoothing and decay estimates for nonlinear diffusion equations

: equations of porous medium type

2006, Oxford lecture series in mathematics and its applications, ISBN 0199202974, Volume 33, xiii, 234

This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the...

Burgers equation | applied mathematics | Delayed regularity | Singular parabolicity | Smoothing | Nonlinearities of power type | Asymptotics | Extinction in finite time | Time decay | Decay rates | Classical heat equation

Burgers equation | applied mathematics | Delayed regularity | Singular parabolicity | Smoothing | Nonlinearities of power type | Asymptotics | Extinction in finite time | Time decay | Decay rates | Classical heat equation

Book

1975, Pure and applied mathematics, a series of monographs and textbooks, ISBN 9780127485409, Volume 67, xiv, 267

Book

1983, ISBN 0387907521, Volume 258., xx, 581

Book

2018, 1, Monographs and research notes in mathematics, ISBN 9781351641364, Volume 1, xix, 240 pages

It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their...

Reaction-diffusion equations | Differential equations, Nonlinear | Differential equations, Partial | Symmetry (Mathematics) | Numerical solutions | Applied Mathematics | Differential Equations

Reaction-diffusion equations | Differential equations, Nonlinear | Differential equations, Partial | Symmetry (Mathematics) | Numerical solutions | Applied Mathematics | Differential Equations

Book

2013, Mathematical surveys and monographs, ISBN 9781470410490, Volume no. 194., xvi, 189

Book

1992, Translations of mathematical monographs, ISBN 0821845705, Volume 114, x, 225

Book

2010, Student mathematical library, ISBN 9780821848296, Volume 55, ix, 156

Book

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 12/2016, Volume 463, pp. 445 - 451

The Fokker–Planck equation (FPE) of the unimolecular reaction with Tsallis distribution is established by means of approximation to the master equation. The...

Master equation | Chemical kinetics | Power-law distribution | ANOMALOUS DIFFUSION | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | MODEL | Chemical reaction, Rate of | Laws, regulations and rules | Analysis

Master equation | Chemical kinetics | Power-law distribution | ANOMALOUS DIFFUSION | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | MODEL | Chemical reaction, Rate of | Laws, regulations and rules | Analysis

Journal Article

1996, 1st ed., Applied mathematics and mathematical computation, ISBN 0412564408, Volume 12., xii, 372

Accurate modelling of the interaction between convective and diffusive processes is one of the commonest challenges in the numerical approximation of partial...

convection | diffusion | fluid dynamics | mathematical models | numerical analysis

convection | diffusion | fluid dynamics | mathematical models | numerical analysis

Book

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. Coverage...

Differential equations, Partial | Fourier series | Boundary value problems

Differential equations, Partial | Fourier series | Boundary value problems

Book

Journal of Mathematical Physics, ISSN 0022-2488, 01/2001, Volume 42, Issue 1, pp. 200 - 212

The Fokker–Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there...

ANOMALOUS DIFFUSION | ASYMMETRIC RANDOM-WALKS | ADVECTION | DYNAMICS | FLIGHTS | EXCHANGE | PHYSICS, MATHEMATICAL | FLOW

ANOMALOUS DIFFUSION | ASYMMETRIC RANDOM-WALKS | ADVECTION | DYNAMICS | FLIGHTS | EXCHANGE | PHYSICS, MATHEMATICAL | FLOW

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2016, Volume 39, Issue 10, pp. 2461 - 2476

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear...

time‐fractional partial differential equations (TFPDEs) | time‐fractional sine‐Gordon equations | boundary elements method (BEM) | time‐fractional telegraph equation | radial basis functions (RBFs) | boundary integral equation method | time‐fractional Fokker–Planck equations | time‐fractional Klein–Gordon equations | dual reciprocity boundary elements method (DRBEM) | time-fractional telegraph equation | time-fractional partial differential equations (TFPDEs) | time-fractional sine-Gordon equations | time-fractional Fokker–Planck equations | time-fractional Klein–Gordon equations | CONVECTION FLOW | MATHEMATICS, APPLIED | ELEMENT-METHOD | TELEGRAPH EQUATION | time-fractional Fokker-Planck equations | SUB-DIFFUSION EQUATION | HIGH-ORDER | SPACE | SCHEME | NUMERICAL-SOLUTION | DRBEM SOLUTION | time-fractional Klein-Gordon equations | SINE-GORDON | Methods | Differential equations | Partial differential equations | Reciprocity | Integral equations | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Boundaries

time‐fractional partial differential equations (TFPDEs) | time‐fractional sine‐Gordon equations | boundary elements method (BEM) | time‐fractional telegraph equation | radial basis functions (RBFs) | boundary integral equation method | time‐fractional Fokker–Planck equations | time‐fractional Klein–Gordon equations | dual reciprocity boundary elements method (DRBEM) | time-fractional telegraph equation | time-fractional partial differential equations (TFPDEs) | time-fractional sine-Gordon equations | time-fractional Fokker–Planck equations | time-fractional Klein–Gordon equations | CONVECTION FLOW | MATHEMATICS, APPLIED | ELEMENT-METHOD | TELEGRAPH EQUATION | time-fractional Fokker-Planck equations | SUB-DIFFUSION EQUATION | HIGH-ORDER | SPACE | SCHEME | NUMERICAL-SOLUTION | DRBEM SOLUTION | time-fractional Klein-Gordon equations | SINE-GORDON | Methods | Differential equations | Partial differential equations | Reciprocity | Integral equations | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Boundaries

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2015, Volume 80, Issue 1-2, pp. 281 - 286

The tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is...

Discrete fractional calculus | Discrete fractional partial difference equations | Discrete anomalous diffusion | ANOMALOUS DIFFUSION | CHAOS | MECHANICS | ENGINEERING, MECHANICAL | Analysis | Differential equations | Resveratrol | Partial differential equations | Difference equations | Diffusion | Fractional calculus | Deltas | Equivalence | Discretization | Mathematical analysis | Tools | Mathematical models | Calculus

Discrete fractional calculus | Discrete fractional partial difference equations | Discrete anomalous diffusion | ANOMALOUS DIFFUSION | CHAOS | MECHANICS | ENGINEERING, MECHANICAL | Analysis | Differential equations | Resveratrol | Partial differential equations | Difference equations | Diffusion | Fractional calculus | Deltas | Equivalence | Discretization | Mathematical analysis | Tools | Mathematical models | Calculus

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2016, Volume 274, pp. 55 - 64

An integral equation approach is proposed to solve the unsteady convection–diffusion equations. In this approach, the second order Adams–Moulton method is...

Convection–diffusion equation | Finite volume element method | Integral equation approach | Convection-diffusion equation | SYSTEM | SCHEME | MATHEMATICS, APPLIED | CYLINDRICAL GEOMETRY | PARTIAL-DIFFERENTIAL-EQUATIONS | FORMULATIONS | FINITE-ELEMENT-METHOD | LAYERS

Convection–diffusion equation | Finite volume element method | Integral equation approach | Convection-diffusion equation | SYSTEM | SCHEME | MATHEMATICS, APPLIED | CYLINDRICAL GEOMETRY | PARTIAL-DIFFERENTIAL-EQUATIONS | FORMULATIONS | FINITE-ELEMENT-METHOD | LAYERS

Journal Article

Contemporary Physics, ISSN 0010-7514, 07/2017, Volume 58, Issue 3, pp. 253 - 261

This work is a self-contained introduction to some basic aspects of the dynamics that occurs in biological populations. It focusses on the proportion (or...

population genetics | stochastic process | evolution | Diffusion analysis | POPULATION | PROBABILITY | PHYSICS, MULTIDISCIPLINARY | FIXATION | Functions (mathematics) | Genetic drift | Populations | Computer simulation | Extinction | Analogue | Biological evolution | Probability theory | Biology | Derivatives | Physics | Biological effects | Random numbers | Fixation | Schrodinger equation | Differential equations | Randomness | Population | Genetics | Drift | Diffusion

population genetics | stochastic process | evolution | Diffusion analysis | POPULATION | PROBABILITY | PHYSICS, MULTIDISCIPLINARY | FIXATION | Functions (mathematics) | Genetic drift | Populations | Computer simulation | Extinction | Analogue | Biological evolution | Probability theory | Biology | Derivatives | Physics | Biological effects | Random numbers | Fixation | Schrodinger equation | Differential equations | Randomness | Population | Genetics | Drift | Diffusion

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2008, Volume 222, Issue 2, pp. 333 - 350

In this paper, we elaborated a spectral collocation method based on differentiated Chebyshev polynomials to obtain numerical solutions for some different kinds...

2D Burgers’ equation | Chebyshev spectral collocation method | 1D Burgers’ equation | Numerical solutions | Coupled Burgers’ equations | System of 2D Burgers’ equations | KdV–Burgers’ equation | KdV-Burgers' equation | 1D Burgers' equation | 2D Burgers' equation | System of 2D Burgers' equations | Coupled Burgers' equations | KdV-Burger' equation | INVARIANT SOLUTIONS | MATHEMATICS, APPLIED | PSEUDO-SPHERICAL SURFACES | SIMILARITY SOLUTIONS | DIFFUSION EQUATION | 1D Bugers' equation | System of 2D Burgers' equation | TRAVELING-WAVE SOLUTIONS | POTENTIAL SYMMETRIES | BACKLUND-TRANSFORMATIONS | NUMERICAL-SOLUTIONS | ADOMIAN DECOMPOSITION METHOD | NONLINEAR EVOLUTION-EQUATIONS

2D Burgers’ equation | Chebyshev spectral collocation method | 1D Burgers’ equation | Numerical solutions | Coupled Burgers’ equations | System of 2D Burgers’ equations | KdV–Burgers’ equation | KdV-Burgers' equation | 1D Burgers' equation | 2D Burgers' equation | System of 2D Burgers' equations | Coupled Burgers' equations | KdV-Burger' equation | INVARIANT SOLUTIONS | MATHEMATICS, APPLIED | PSEUDO-SPHERICAL SURFACES | SIMILARITY SOLUTIONS | DIFFUSION EQUATION | 1D Bugers' equation | System of 2D Burgers' equation | TRAVELING-WAVE SOLUTIONS | POTENTIAL SYMMETRIES | BACKLUND-TRANSFORMATIONS | NUMERICAL-SOLUTIONS | ADOMIAN DECOMPOSITION METHOD | NONLINEAR EVOLUTION-EQUATIONS

Journal Article