Existence of positive solutions for some nonlinear parabolic equations in the half space by Abdeljabbar Ghanmi

“…The function f is nonnegative continuous non-increasing, and the potential p is nonnegative and satisfies some hypotheses related to the parabolic Kato class. We use potential theory arguments to prove our main result.…”
Get full text

Some new generalized integral transformations and their application in differential equations theory by Oleg A Repin, Svetlana M Zaikina

“…We present new integral transforms, generalized the classical Laplace, Stieltjes and Widder integral transforms in the potential theory. The (τ, β)-generalized confluent hypergeometric functions are the kernels of these integral transforms. …”
Get full text

Investigation of boundary conditions influence on stability of coaxial cylindrical shells interacting with flowing fluid by S. A. Bochkarev, S. V. Lekomtsev

“…The fluid is described in terms of potential theory. With this approach, the stated problem reduces to simultaneous solving of four sets of equations using the finite element method. …”
Get full text

Three dimensional analyses of cracks and defects by Zhang, Tonglong

“…Recently Fabrikant, based on Green's function approach and some of his new results in potential theory, solved crack and contact problems in a completely new approach. …”
Get full text

The Skorokhod embedding problem and its offspring by Obloj, J

“…A certain unification of proofs, based on one-dimensional potential theory, is made. Some new facts which appeared in a natural way when different solutions were cross-examined, are reported. …”

Application of concentrated solution theory and core potential to ion exchange media by Jung, T

“…Corrections to electrochemical-potential differentials (dμ_i) are derived by combining core-potential theory with the Boltzmann distribution, in accordance with Goyal and Monroe's treatment. …”

Investigation on seakeeping performance of an oil tanker on regular waves by Bianca Elena Roșca, Săndița Păcuraru

“…The numerical simulation was performed using a 3D diffrac-tion/radiation potential theory 3-D panel software. The analysis concerns the full loading case of the ship at zero and design speed. …”
Get full text

Fourier spectra of measures associated with algorithmically random Brownian motion by Willem Louw Fouché, Safari Mukeru, George Davie

“…The study also necessitates a closer look at the potential theory over fractals from a computable point of view.…”
Get full text

On application of three-dimensional linearized potential-flow model for shallow-water planing by Konstantin I. Matveev

“…In this study, a three-dimensional steady linearized model based on the potential theory is applied to model flat planing surfaces at finite water depth and finite Froude numbers. …”
Get full text

Aleksandr Lyapunov, the man who created the modern theory of stability by László Hatvani

“…We recount the main fields of his scientific activity (stability theory, potential theory, probability theory, shape of planets) concerning stability theory and chaos in details.…”
Get full text

Ellipsoid movement in ideal or viscous fluid by Petrov Alexander, Lopushanski Mariana

“…With the help of the Newton potential theory it is shown that the complete solution of this problem may be expressed through a single function of two variables, which, in its turn, can be expressed through two well-known elliptic functions - E(x; y) and F(x; y). …”
Get full text

Positive blowup solutions for some fractional systems in bounded domains by Ramzi Alsaedi

“…Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of a positive continuous weak solution for the fractional system $$ ( -Delta )^{alpha/2}u+ p(x)u^{sigma }v^{r}=0,quad (-Delta)^{alpha/2}v+q(x)u^{s}v^{eta }=0 $$ in a bounded $ C^{1,1}$-domain D in $mathbb{R}^{n}$ $(ngeq 3)$, subject to Dirichlet conditions, where $0<alpha <2$, $sigma ,eta geq 1$, $s,rgeq 0$. …”
Get full text

The modified quadrature method for Laplace equation with nonlinear boundary conditions by Hu Li

“…Here, the numerical solutions for Laplace equation with nonlinear boundary conditions is studied. Based on the potential theory, the problem can be converted into a nonlinear boundary integral equation. …”
Get full text

Persisting randomness in randomly growing discrete structures: graphs and search trees by Rudolf Grübel

“…Using examples from random graph theory and search algorithms we show how such persistence of randomness can be detected and quantified with techniques from discrete potential theory. We also show that this approach can be used to obtain strong limit theorems in cases where previously only distributional convergence was known.…”
Get full text

Integrals of Legendre polynomials over half range and their relation to the electrostatic potential in hemispherical geometry by Orion Ciftja

“…In this work, we consider a case study that arises from potential theory where absence of a full spherical symmetry gives rise to expressions involving Legendre polynomials constrained in an interval that is different from the usual range in which they are orthogonal. …”
Get full text

Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed type by Chen, G-QG

“…The main focus is on Morawetz’s fundamental work on the nonexistence of continuous transonic flows past profiles, Morawetz’s program regarding the construction of global steady weak transonic flow solutions past profiles via compensated compactness, and a potential theory for regular and Mach reflection of a shock at a wedge. …”

Mechanisms of the Volume Filling of Micropores during the Adsorption of Vapours by O. Kadlec

“…It is concluded, that the validity of the potential theory for MVF is based on the equality of the p f al and the standard liquid state p o l pressures (mechanism MVF 1). …”
Get full text

Transmission coefficients of a floating rectangular breakwater with porous side plates by Il-Hyoung Cho

“…The interaction between incident waves and a floating rectangular breakwater with the vertical porous side plates has been investigated in the context of the two-dimensional linear potential theory. The matched eigenfunction expansion method(MEEM) for multiple domains is applied to obtain the analytic solutions. …”
Get full text

Existence of bounded positive solutions of a nonlinear differential system by Sabrine Gontara

“…In this article, we study the existence and nonexistence of solutions for the system $$displaylines{ frac{1}{A}(Au')'=pu^{alpha }v^{s}quad hbox{on }(0,infty ), cr frac{1}{B}(Bu')'=qu^{r}v^{eta }quad hbox{on }(0,infty ), cr Au'(0)=0,quad u(infty )=a>0, cr Bv'(0)=0,quad v(infty )=b>0, }$$ where $alpha ,eta geq 1$, $s,rgeq 0$, p,q are two nonnegative functions on $(0,infty )$ and A, B satisfy appropriate conditions. Using potential theory tools, we show the existence of a positive continuous solution. …”
Get full text

On the interaction of wind and steep gravity wave groups using Miles' and Jeffreys' mechanisms by J. Touboul, C. Kharif, E. Pelinovsky, J.-P. Giovanangeli

“…The linear theory is based on the Schrödinger equation while the nonlinear approach is developed numerically within the framework of the potential theory. The interaction between the chirped wave packet and wind is described by the Miles' mechanism. …”
Get full text