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12/2017, Mathematics for Industry Ser., ISBN 3319679422, Volume 31
Annotation This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical... 
Web Resource
2018, Mathematics for Industry, ISBN 3319679422, Volume 31, 299
This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. 
Engineering | Theoretical and Applied Mechanics | Mathematical Applications in the Physical Sciences | Industrial Chemistry/Chemical Engineering | Partial Differential Equations | Computer Appl. in Life Sciences
eBook
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2018, Volume 41, Issue 3, pp. 1074 - 1082
In the current paper, we consider a stochastic parabolic equation that actually serves as a mathematical model describing the operation of an electrostatic... 
electrostatic MEMS | quenching | stochastic semilinear partial differential equations | touchdown | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | DEVICES | DRIVEN | Interrupted quenching | Mathematical models | Partial differential equations | Quenching (cooling)
Journal Article
Discrete and Continuous Dynamical Systems, ISSN 1078-0947, 05/2012, Volume 32, Issue 5, pp. 1723 - 1746
We consider a nonlocal parabolic equation associated with Dirichlet boundary and initial conditions arising in MEMS control. First, we investigate the... 
Touchdown | Morse index | Electrostatic MEMS | Quenching | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | BEHAVIOR | touchdown | DEVICE | SINGULAR NONLINEARITY | quenching | COMPACTNESS | ELLIPTIC PROBLEM
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2015, Volume 38, Issue 16, pp. 3564 - 3574
In this paper, we consider a non‐local stochastic parabolic equation that actually serves as a mathematical model describing the adiabatic shear banding... 
blow‐up | maximum principle | shear band formation | non‐local | stochastic partial differential equations | non-local | blow-up | MATHEMATICS, APPLIED | SPDES | PARTIAL-DIFFERENTIAL-EQUATIONS | Explosive forming | Partial differential equations | Maximum principle | Mathematical models | Formations | Explosions | Stochasticity | Slip bands
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 02/2019, Volume 462, pp. 184 - 193
•The linear model accounts for the overall epigenetic inheritance of DNA methylation patterns and dynamics.•The nonlinear model can predict the hypomethylated... 
Hypomethylation | Sensitivity analysis | Hypermethylation | CpG island | Gene promoter bistability | CpG dyads | PATTERNS | MECHANISMS | INACTIVATION | METHYLTRANSFERASES | DEMETHYLATION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | TISSUES | INHERITANCE | EXPRESSION | FOLATE | INSIGHTS | Epigenetic inheritance | Enzymes | DNA | Molecular dynamics | Mathematical models | Methylation | Alzheimer's disease
Journal Article
Nonlinearity, ISSN 0951-7715, 03/2017, Volume 30, Issue 5, pp. 1734 - 1761
The purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activator-inhibitor system known as a... 
turing instability | invariant regions | pattern formation | diffusion-driven blow-up | shadow-system | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | HEAT-EQUATIONS | PHYSICS, MATHEMATICAL | TIME BLOW-UP | Mathematics - Analysis of PDEs
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2009, Volume 40, Issue 5, pp. 1852 - 1881
We consider a special case of the Patlak-Keller-Segel system in a disc, which arises in the modeling of chemotaxis phenomena. For a critical value of the total... 
Grow-up | Chemotaxis system | Critical mass | Sub-/supersolutions | SINGULAR STEADY-STATE | SEMILINEAR HEAT-EQUATION | MATHEMATICS, APPLIED | RADIALLY SYMMETRIC-SOLUTIONS | NONLINEARITY | grow-up | critical mass | chemotaxis system | CHEMOTAXIS MODEL | sub-/supersolutions | 8-PI-PROBLEM | DIFFUSION | BLOW-UP | PARABOLIC EQUATION | AGGREGATION
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 2, pp. 954 - 983
Journal Article
Journal of theoretical biology, 11/2018, Volume 462, p. 184
DNA methylation is a key epigenetic process which has been intimately associated with gene regulation. In recent years growing evidence has associated DNA... 
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 04/2019, Volume 467, pp. 87 - 99
•Aberrant DNA methylation patterns are a hallmark of diseases, such as cancer, Alzheimer’s disease, and cardiovascular disease, and mathematical analysis of... 
DNA methylation | Parameter estimation | Gene promoter | Model selection | CpG dyads | DNMTS | METHYLTRANSFERASES | DEMETHYLATION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EXPRESSION | Numerical analysis | Analysis | DNA | Mathematical models | Methylation | Epidemiology | Alzheimer's disease
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 03/2015, Volume 35, Issue 3, pp. 1009 - 1037
In this work we study the semilinear wave equation of the form u(tt) = u(xx) + lambda/(1 - u)(2) , with homogeneous Dirichlet boundary conditions and suitable... 
Similarity analysis | Electrostatic MEMS | Quenching of solution | For-mal asymptotic | Hyperbolic problems | MATHEMATICS, APPLIED | formal asymptotic | quenching of solution | CAPACITOR | DEVICE | DIFFERENTIAL-EQUATIONS | TOUCHDOWN | MATHEMATICS | hyperbolic problems | similarity analysis | DIELECTRIC-PROPERTIES | DYNAMICS | BLOW-UP | FOCUSING NONLINEARITY
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 06/2016, Volume 138, pp. 189 - 206
We consider a nonlocal parabolic model for a micro–electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is... 
Electrostatic MEMS | Touchdown | Quenching | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR HEAT-EQUATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | BLOW-UP | Microelectromechanical systems | Numerical analysis
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 06/2015, Volume 44, pp. 30 - 33
In this paper we revisit Hamilton’s normalized Ricci flow, which was thoroughly studied via a PDE approach in Kavallaris and Suzuki (2010). Here we provide an... 
Ricci flow | Non-local parabolic problems | Non-local parabolic | problems | MATHEMATICS, APPLIED | GAUSSIAN CURVATURE | BEHAVIOR | MANIFOLDS | UNIQUENESS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 09/2013, Volume 66, Issue 4, pp. 512 - 524
A novel approach is developed to prove the existence of δ∗, the supremum of the spectrum of a non-local elliptic problem associated with homogeneous Robin and... 
Bifurcation parameters | Non-local elliptic problems | Moving plane method | MATHEMATICS, APPLIED | DIFFUSION | TIME | BLOW-UP | PARABOLIC PROBLEMS
Journal Article
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), ISSN 0272-4960, 02/2014, Volume 79, Issue 1, pp. 1 - 21
We continue the study on a reaction-diffusion system with non-local terms, which arises as a mean field limit of a master equation using a reaction radius.... 
reaction radius | non-local | reaction-diffusion systems | MATHEMATICS, APPLIED | Mathematical analysis | Convergence
Journal Article
European Journal of Applied Mathematics, ISSN 0956-7925, 12/2011, Volume 22, Issue 6, pp. 533 - 552
In this paper we establish an existence and uniqueness result for a class of non-local elliptic differential equations with the Dirichlet boundary conditions,... 
Elliptic Differential Equations | Non-Local Problems | Maximum Principle | EQUATIONS | MATHEMATICS, APPLIED | POSITIVITY | Applied mathematics | Boundary conditions | Differential equations | Elliptic differential equations | Mathematical analysis | Uniqueness | Maximum principle | Dirichlet problem | Iterative methods | Convergence
Journal Article
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), ISSN 0272-4960, 06/2013, Volume 78, Issue 3, pp. 614 - 632
A reaction-diffusion system with non-local term arises as a mean field limit of a master equation using reaction radius. We show that a two-phase Stefan... 
reaction radius | non-local | reaction-diffusion systems | CHEMICAL-REACTION INTERFACE | MATHEMATICS, APPLIED | Mathematical analysis | Chemical reactions | Convergence
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 72, Issue 5, pp. 2300 - 2317
This paper is concerned with a parabolic equation with a non-local term defined on a compact two-dimensional Riemannian surface Ω . If the total mass of the... 
Ricci flow | Non-local parabolic problems | EXISTENCE | STATISTICAL-MECHANICS | MATHEMATICS, APPLIED | BEHAVIOR | INEQUALITY | UNIQUENESS | MATHEMATICS | DIMENSIONS | R-2 | DYNAMICS | CONVERGENCE | MANIFOLDS
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2008, Volume 15, Issue 3, pp. 363 - 386
We study the electrostatic MEMS-device equation, $$u_{t} -\Delta u = \frac{\lambda |x|^{\beta}}{(1-u)^{p}}$$ , with Dirichlet boundary condition. First, we... 
touchdown-quenching | Electrostatic MEMS | Analysis | Primary 35K55, 35J60 | Mathematics | Secondary 74H35, 74G55, 74K15 | Morse idex | Touchdown-quenching | MATHEMATICS, APPLIED | BLOW-UP | Microelectromechanical systems | Football teams | Universities and colleges
Journal Article
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