Results 121 to 130 of about 106,170 (279)

Multiple solutions for semilinear elliptic boundary value problems at resonance

Electronic Journal of Differential Equations, 1995
successful in proving the existence of weak solutions for semilinear elliptic boundary value problems at resonance. One technique involves a variational approach where solutions are characterized as saddle points for a related functional.
Steve B. Robinson
doaj  

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Front Propagation Through a Perforated Wall

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki, François Hamel, Hiroshi Matano   +2 more
wiley   +1 more source

Failure characteristics and the energy criterion of rock with a through‐going joint under true‐triaxial unloading conditions: Insights from the DEM model

Deep Underground Science and Engineering, EarlyView.
The rock failure mode is significantly influenced by the contributing factors, such as the joint inclination, the initial confining pressure, and the unloading point. We found six typical rock failure modes after a large number of numerical tests. Abstract Excavation unloading damages rock masses, with preferential failure along geological defects in ...
Fei Liu, Changhui Liang, Sijia Liu, Yongjun Zhang, Luo Wang   +4 more
wiley   +1 more source

Integral representations of solutions of coercive solvable problems for the Laplace equation

Boundary Value Problems
Modeling of many stationary physical processes is reduced to the study of boundary value problems for elliptic equations. Starting with the works of A.V. Bitsadze and A.A. Samarskiy, well-posed, but not necessarily boundary value problems for the Laplace
Tynysbek Kal’menov
doaj   +1 more source

Generalized Matsuoka–Nakai criterion considering hydrostatic pressure dependence in the brittle–ductile region

Deep Underground Science and Engineering, EarlyView.
Three sets of strength data were selected, including hydrostatic pressure independent within the brittle region (HPI‐B), hydrostatic pressure dependent within the brittle region (HPD‐B), and hydrostatic pressure dependent within the brittle–ductile region (HPD‐BD). For HPI type, the failure envelope within the deviatoric plane remains constant.
Jiacun Liu, Junjie Xiao, Dongping Liu, Ying Xu   +3 more
wiley   +1 more source

Random finite element analysis on ground subsidence caused by tunnel excavation in karst regions with spatial variable soil

Deep Underground Science and Engineering, EarlyView.
This study investigates ground subsidence during tunnel excavation in karst areas, highlighting the combined effects of karst cave proximity, cave size, and soil spatial variability. Findings suggest that shorter cave distances and larger cave sizes increase subsidence variability, and a modified Peck formula is proposed for more accurate subsidence ...
Zhenghong Su, Yong Fu, Miaomiao Sun, Kailin Ding, Ying Zhao   +4 more
wiley   +1 more source

The impact of forced closure on proppant distribution of hydraulic fracturing in shale formations

Deep Underground Science and Engineering, EarlyView.
Research findings demonstrate that implementing forced closure within shale formations can remarkably mitigate proppant settlement, concurrently increasing the effective propped surface area from 29.74% to 38.68%. Abstract Forced closure is widely used in conventional oil and gas reservoirs to promote uniform proppant placement.
Tongxuan Gu, Hanyi Wang, Quan Gan, Shuang Zheng   +3 more
wiley   +1 more source

Existence and uniqueness of solutions to a semilinear elliptic system

Electronic Journal of Differential Equations, 2009
In this article, we show the existence and uniqueness of smooth solutions for boundary-value problems of semilinear elliptic systems.
Ying Cui, Zu-Chi Chen
doaj  

Gaborlet‐guided sparse filtering: A novel intelligent method for lithology identification by vibration signals while drilling

Deep Underground Science and Engineering, EarlyView.
The flowchart illustrates rock specimen testing, vibration signal acquisition, and feature extraction with Gaborlet and sparse filtering for classification. Abstract Traditional lithology identification methods mainly rely on core sampling and well‐logging data.
Jian Hao, Danqi Zhang, Zhenqi Song, Jinrui Wang, Qi Wang, Heqing Liu   +5 more
wiley   +1 more source