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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
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
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
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
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
Journal Article
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
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
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
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)
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
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 1, pp. 628 - 647
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
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
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
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
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2011, Volume 80, Issue 273, pp. 89 - 117
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
Journal Article
Journal of Physical Chemistry A, ISSN 1089-5639, 08/2017, Volume 121, Issue 33, p. 6341
Journal Article
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