2015, 2nd edition., Advances in applied mathematics, ISBN 9781482251029, xvii, 667

About the Previous Edition"Roughly speaking, Green's functions constitute infinitesimal matrix coefficients that one can use to solve linear nonhomogeneous...

Green's functions | Green-Funktion

Green's functions | Green-Funktion

Book

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

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 06/2019, Volume 29, Issue 7, pp. 1279 - 1348

In this paper, we are interested in the mathematical model of MEMS devices which is presented by the following equation on (0,T) x Omega: partial...

asymptotic behavior | Blowup solution | semilinear heat equation | non-variational heat equation | touch-down profile | non-variational heat equation by MEMS model | quenching solution | touch-down phenomenon | stability | blowup profile | MATHEMATICS, APPLIED | BLOW-UP PROFILE | NONLINEAR HEAT-EQUATION | POINTS

asymptotic behavior | Blowup solution | semilinear heat equation | non-variational heat equation | touch-down profile | non-variational heat equation by MEMS model | quenching solution | touch-down phenomenon | stability | blowup profile | MATHEMATICS, APPLIED | BLOW-UP PROFILE | NONLINEAR HEAT-EQUATION | POINTS

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 11/2017, Volume 53, Issue 4, pp. 1991 - 2004

Journal Article

Osaka Journal of Mathematics, ISSN 0030-6126, 01/2018, Volume 55, Issue 1, pp. 117 - 163

Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this...

MATHEMATICS | KERNEL | HEAT-EQUATION

MATHEMATICS | KERNEL | HEAT-EQUATION

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2019, Volume 276, Issue 4, pp. 1145 - 1200

In this paper, we prove the existence of an initial trace Tu for any positive solution u to the semilinear fractional diffusion equation...

Singularities | Fractional heat equation | Initial trace | MATHEMATICS | HEAT-EQUATIONS | REGULARITY | COMPLETE CLASSIFICATION | DELTA-U

Singularities | Fractional heat equation | Initial trace | MATHEMATICS | HEAT-EQUATIONS | REGULARITY | COMPLETE CLASSIFICATION | DELTA-U

Journal Article

7.
An introduction to Laplacian spectral distances and kernels

: theory, computation, and applications

2017, 1, Synthesis lectures on visual computing : Computer graphics, animation, computational photography, and imaging, ISBN 9781681731391, Volume 29, xxv, 113 pages

In geometry processing and shape analysis, several applications have been addressed through the properties of the Laplacian spectral kernels and distances,...

Geometry | Harmonic functions | Computer simulation | Computer graphics | Data processing | Mathematics | Shapes | Laplacian operator | Computing and Processing | General Topics for Engineers | COMPUTERS / Data Visualization | MATHEMATICS / Numerical Analysis | MATHEMATICS / Geometry / General

Geometry | Harmonic functions | Computer simulation | Computer graphics | Data processing | Mathematics | Shapes | Laplacian operator | Computing and Processing | General Topics for Engineers | COMPUTERS / Data Visualization | MATHEMATICS / Numerical Analysis | MATHEMATICS / Geometry / General

Book

Memoirs of the American Mathematical Society, ISSN 0065-9266, 07/2016, Volume 242, Issue 1146, pp. 1 - 96

We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on observability results through Carleman estimates for the...

MATHEMATICS | DIMENSIONAL HEAT-EQUATION | OPERATORS | UNIQUE CONTINUATION

MATHEMATICS | DIMENSIONAL HEAT-EQUATION | OPERATORS | UNIQUE CONTINUATION

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2019, Volume 277, Issue 5, pp. 1531 - 1579

In this paper, we consider the following complex-valued semilinear heat equation∂tu=Δu+up,u∈C, in the whole space Rn, where p∈N,p≥2. We aim at constructing for...

Blowup profile | Non variation heat equation | Semilinear complex heat equation | Blowup solution | UP PROFILE | MATHEMATICS | STABILITY | BEHAVIOR | CONSTRUCTION | MODEL

Blowup profile | Non variation heat equation | Semilinear complex heat equation | Blowup solution | UP PROFILE | MATHEMATICS | STABILITY | BEHAVIOR | CONSTRUCTION | MODEL

Journal Article

2017, London Mathematical Society lecture note series, ISBN 1108125603, Volume 438, xi, 226 pages

This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic...

Markov processes | Graph theory | Heat equation | Random walks (Mathematics)

Markov processes | Graph theory | Heat equation | Random walks (Mathematics)

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 382, Issue 1, pp. 426 - 447

We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ t α u ( x , t ) = L u ( x , t ) , where 0 < α ⩽ 2 , where L is a...

Fractional diffusion equation | Initial value/boundary value problem | Well-posedness | Inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATION | HEAT-EQUATION | Universities and colleges

Fractional diffusion equation | Initial value/boundary value problem | Well-posedness | Inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATION | HEAT-EQUATION | Universities and colleges

Journal Article

2016, Second edition, ISBN 047075625X, xiii, 450 pages

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 1, pp. 628 - 647

We present an operational method to obtain solutions for differential equations, describing a broad range of physical problems, including ordinary non-integer...

Hyperbolic heat equation | Inverse operator | Hermite and Laguerre polynomials | Fokker–Planck equation | Differential equation | MATHEMATICS, APPLIED | PLANAR UNDULATOR | ORDER HEAT-EQUATION | Fokker-Planck equation | HERMITE-POLYNOMIALS | RADIATION | MATHEMATICS | CONSTANT MAGNETIC-FIELD | ACCOUNT | REPRESENTATION-THEORY | HIGH HARMONIC-GENERATION | Differential equations

Hyperbolic heat equation | Inverse operator | Hermite and Laguerre polynomials | Fokker–Planck equation | Differential equation | MATHEMATICS, APPLIED | PLANAR UNDULATOR | ORDER HEAT-EQUATION | Fokker-Planck equation | HERMITE-POLYNOMIALS | RADIATION | MATHEMATICS | CONSTANT MAGNETIC-FIELD | ACCOUNT | REPRESENTATION-THEORY | HIGH HARMONIC-GENERATION | Differential equations

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 3, pp. A1274 - A1300

A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities...

Heat equation | Adaptive mesh refinement | Fast Gauss transform | fast Gauss transform | MATHEMATICS, APPLIED | ERROR ESTIMATE | KERNEL | heat equation | APPROXIMATION | POISSON SOLVER | HEAT-EQUATION | ALGORITHM | adaptive mesh refinement | POTENTIALS | MATHEMATICS AND COMPUTING

Heat equation | Adaptive mesh refinement | Fast Gauss transform | fast Gauss transform | MATHEMATICS, APPLIED | ERROR ESTIMATE | KERNEL | heat equation | APPROXIMATION | POISSON SOLVER | HEAT-EQUATION | ALGORITHM | adaptive mesh refinement | POTENTIALS | MATHEMATICS AND COMPUTING

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 03/2017, Volume 65, pp. 83 - 89

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given...

Fundamental solution | Parabolic heat equation | MATHEMATICS, APPLIED

Fundamental solution | Parabolic heat equation | MATHEMATICS, APPLIED

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 12/2015, Volume 107, pp. 191 - 198

We prove a variant of the central limit theorem for a sequence of i.i.d. random variables ξj, perturbed by a stochastic sequence of linear transformations Aj,...

Half-relaxed limits | [formula omitted]-heat equation | Central limit theorem | Model uncertainty | Viscosity solution | G-heat equation | C-heat equation | VISCOSITY SOLUTIONS | STATISTICS & PROBABILITY

Half-relaxed limits | [formula omitted]-heat equation | Central limit theorem | Model uncertainty | Viscosity solution | G-heat equation | C-heat equation | VISCOSITY SOLUTIONS | STATISTICS & PROBABILITY

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 12/2017, Volume 355, Issue 12, pp. 1215 - 1235

We are interested in the exact null controllability of the equation ∂tf−∂x2f−x2∂y2f=1ωu, with control u supported on ω. We show that, when ω does not intersect...

MATHEMATICS | HEAT-EQUATION | Analysis of PDEs | Mathematics

MATHEMATICS | HEAT-EQUATION | Analysis of PDEs | Mathematics

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2011, Volume 80, Issue 273, pp. 89 - 117

We study the error of the Euler scheme applied to a stochastic partial differential equation. We prove that, as is often the case, the weak order of...

Error rates | Approximation | Partial differential equations | Heat equation | Spacetime | Differential equations | Integration by parts | White noise | Calculus | Stochastic heat equation | Weak order | Euler scheme | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | PDES | FINITE-ELEMENT METHODS | DRIVEN | LATTICE APPROXIMATIONS | HEAT-EQUATION | DISCRETIZATION SCHEMES | ADDITIVE NOISE | CONVERGENCE | stochastic heat equation | TIME WHITE-NOISE

Error rates | Approximation | Partial differential equations | Heat equation | Spacetime | Differential equations | Integration by parts | White noise | Calculus | Stochastic heat equation | Weak order | Euler scheme | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | PDES | FINITE-ELEMENT METHODS | DRIVEN | LATTICE APPROXIMATIONS | HEAT-EQUATION | DISCRETIZATION SCHEMES | ADDITIVE NOISE | CONVERGENCE | stochastic heat equation | TIME WHITE-NOISE

Journal Article

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, Volume 10, Issue 2, pp. 131 - 189

Consider the Cauchy problem u −u −F(u)=0;x∈ℝ,t>0u(x,0)=u (x);x∈ℝwhere u (x) is continuous, nonnegative and bounded, and F(u) = u with p > 1, or F(u) = e ....

asymptotic behaviour of solutions | Semilinear diffusion equations | blow-up | MATHEMATICS, APPLIED | BLOW-UP | ASYMPTOTIC BEHAVIOR OF SOLUTIONS | HEAT-EQUATIONS | SEMILINEAR DIFFUSION EQUATIONS

asymptotic behaviour of solutions | Semilinear diffusion equations | blow-up | MATHEMATICS, APPLIED | BLOW-UP | ASYMPTOTIC BEHAVIOR OF SOLUTIONS | HEAT-EQUATIONS | SEMILINEAR DIFFUSION EQUATIONS

Journal Article

Journal of Physical Chemistry A, ISSN 1089-5639, 08/2017, Volume 121, Issue 33, p. 6341

Journal Article

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