Results 101 to 110 of about 255,795 (302)

Blow-up of H1 solution for the nonlinear Schrödinger equation

, 1991
We consider the blow-up of the solution in H1 for the following nonlinear Schrödinger equation: i∂∂tu + Δu = −¦u¦p − 1u, x ϵ Rn, t ⩾ 0, (∗) u(0, x) = u0(X), x ϵ Rn, t = 0, where n ⩾2 and 1 + 4/n ⩽ p < min {(n + 2)(n − 2), 5}. We prove that if the initial
Ogawa, Takayoshi, Tsutsumi, Yoshio
core   +1 more source

Endoplasmic Reticulum Geometry Dictates Neuronal Bursting via Calcium Store Refill Rates and Exposes Selective Neuronal Vulnerability

Advanced Science, EarlyView.
The ER's continuous tubular network is maintained by ER‐shaping proteins whose mutation or dysregulation contributes to neurodegenerative diseases. Here, we show that ER morphology sets the speed of Ca2+ store replenishment between firing events. Disrupting ER continuity slows intra‐ER Ca2+ redistribution from extracellular refill (SOCE) sites, driving
Valentina Davi, Pierre Parutto, Yuyi Zhang, Tasuku Konno, Cecile Crapart, Raquel Pereira, John P. Franklin, Mosab Ali Awadelkareem, Daniel C Maddison, Michael J. Devine, Edgar R. Gomes, Joseph Chambers, Elena Koslover, Edward Avezov   +13 more
wiley   +1 more source

Some properties of solutions for an isothermal viscous Cahn–Hilliard equation with inertial term

Boundary Value Problems, 2018
In this paper, we study the global existence and blow-up of solutions for an isothermal viscous Cahn–Hilliard equation with inertial term, which arises in isothermal fast phase separation processes.
Changchun Liu, Jiaojiao Wang
doaj   +1 more source

Blow-up Estimates of the Positive Solution of a Parabolic System

Journal of Mathematical Analysis and Applications, 2001
The authors study blow-up of a system of two heat equations in a ball coupled by nonlinear boundary conditions. They show that radially symmetric time-increasing positive solutions blow up with the selfsimilar rate if the four exponents from the boundary conditions satisfy certain conditions.
Pedersen, Michael, Lin, Zhigui
openaire   +2 more sources

On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions [PDF]

, 1999
summary:We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend
Boni, Théodore K.
core  

Machine‐Learning Microfluidic Minute‐Scale Microorganism Metrics Monitoring(M6)

Advanced Science, EarlyView.
ABSTRACT On‐site monitoring of microorganisms remains challenging because of low concentrations, strong background interference, and dynamic aerosol diffusion, particularly for aerosol‐transmitted pathogens. Here, we report a rapid detection platform that integrates a Puri‐focusing microfluidic chip, electrochemical impedance spectroscopy (EIS), and ...
Ning Yang, Jiahao Ding, Si Chen, Lijie Yan, Shichao Ding, Lavonda Li, Junyi Sun, Haodong Liu, Tongge Li, Ning Liu, Mingji Wei, Xiaoyong Zhu, Xiaobo Zou, Shouqi Yuan, Xingcai Zhang   +14 more
wiley   +1 more source

Global well-posedness of solutions to a class of heat equation under dynamical type boundary conditions [PDF]

Arab Journal of Mathematical Sciences
PurposeBy employing the Galerkin approximation and a family of potential wells, we establish the existence of a global solution and finite-time blow-up under certain suitable conditions. Additionally, we provide results concerning the asymptotic behavior
Mahmoud El Ahmadi, Anass Lamaizi, Mohammed Barghouthe   +2 more
doaj   +1 more source

Printable Conductive Hydrogels for Electrochemical Biosensing and Soft Bioelectronic Interfaces

Advanced Science, EarlyView.
Flexible, conductive hydrogels that integrate printability, mechanical tunability, biocompatibility, and electronic performance remain challenging to achieve. Here, we develop 3D‐printable poly(ethylene glycol)–poly(pyrrole)‐ hydrogels with tissue‐like mechanics, high cytocompatibility, and robust electrochemical function.
Lukas Hein, Renan Colucci, Xin Wei, Tsvetomir Ivanov, Katharina Landfester, Ulrike Kraft, Maria Villiou   +6 more
wiley   +1 more source

Blow-up and global existence for nonlinear reaction-diffusion equations under Neumann boundary conditions

Journal of Inequalities and Applications, 2016
In this paper, we study the blow-up and global solutions of the following nonlinear reaction-diffusion equations under Neumann boundary conditions: { ( g ( u ) ) t = ∇ ⋅ ( a ( u ) b ( x ) ∇ u ) + f ( x , u ) in  D × ( 0 , T ) , ∂ u ∂ n = 0 on  ∂ D × ( 0 ,
Juntang Ding
doaj   +1 more source

Blow-Up of the Solution for some Higher Order Hyperbolic and Neutral Evolution Systems

, 2011
In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher-order nonlinear hyperbolic and parabolic evolution equation in finite time.
Ning Chen, Ji Qian Chen
core   +1 more source