scholarly journals Global existence and blow-up of solutions for a Non-Newton polytropic filtration system with special volumetric moisture content

2016 ◽  
Vol 71 (5) ◽  
pp. 1163-1172 ◽  
Author(s):  
Jun Zhou
Keyword(s):  
Moisture Content ◽  
Global Existence ◽  
Blow Up ◽  
Volumetric Moisture Content ◽  
Filtration System

scholarly journals GLOBAL EXISTENCE AND BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLOCAL SOURCE

2008 ◽  
Vol 50 (01) ◽  
pp. 13 ◽  
Author(s):  
JUN ZHOU ◽  
CHUNLAI MU
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Nonlocal Source ◽  
Filtration System

Global existence and blow-up for non-Newton polytropic filtration system with nonlocal source

2009 ◽  
Vol 50 ◽  
Author(s):  
Jun Zhou ◽  
Chunlai Mu
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Nonlocal Source ◽  
Filtration System

scholarly journals GLOBAL EXISTENCE AND BLOW-UP FOR NON-NEWTON POLYTROPIC FILTRATION SYSTEM COUPLED WITH LOCAL SOURCE

2009 ◽  
Vol 51 (1) ◽  
pp. 39-47 ◽  
Author(s):  
JUN ZHOU ◽  
CHUNLAI MU
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Finite Time ◽  
Blow Up ◽  
Local Source ◽  
Filtration System

AbstractThis paper deals with the global existence and blow-up properties of the following non-Newton polytropic filtration system coupled with local source: ut − Δm,pu = avα, vt − Δn,qv = buβ. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depending on the initial data and the relations between αβ and mn(p − 1)(q − 1).

Transfer of the unit of oil volumetric moisture content to measuring devices

2019 ◽  
pp. 5-8
Author(s):  
A.V. Voronenko ◽  
◽  
V.V. Averin ◽  
D.E. Ushatkin ◽  
◽  
...  
Keyword(s):  
Moisture Content ◽  
Measuring Devices ◽  
Volumetric Moisture Content

Global existence and blow-up of weak solutions for a pseudo-parabolic equation with high initial energy

2020 ◽  
Vol 104 ◽  
pp. 106270
Author(s):  
Xiangyu Zhu ◽  
Bin Guo ◽  
Menglan Liao
Keyword(s):  
Parabolic Equation ◽  
Global Existence ◽  
Weak Solutions ◽  
Blow Up ◽  
Initial Energy

scholarly journals Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongbin Wang ◽  
Binhua Feng
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Critical Case ◽  
Blow Up ◽  
Critical Mass ◽  
Choquard Equation ◽  
Power Type ◽  
Scale Invariant ◽  
Nonlinear Schrödinger ◽  
Sharp Thresholds

AbstractIn this paper, we consider the sharp thresholds of blow-up and global existence for the nonlinear Schrödinger–Choquard equation $$ i\psi _{t}+\Delta \psi =\lambda _{1} \vert \psi \vert ^{p_{1}}\psi +\lambda _{2}\bigl(I _{\alpha } \ast \vert \psi \vert ^{p_{2}}\bigr) \vert \psi \vert ^{p_{2}-2}\psi . $$iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. We derive some finite time blow-up results. Due to the failure of this equation to be scale invariant, we obtain some sharp thresholds of blow-up and global existence by constructing some new estimates. In particular, we prove the global existence for this equation with critical mass in the $L^{2}$L2-critical case. Our obtained results extend and improve some recent results.

scholarly journals Blow-up and global existence for semilinear parabolic systems with space-time forcing terms

2021 ◽  
Vol 147 ◽  
pp. 110982
Author(s):  
Ahmad Z. Fino ◽  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Parabolic Systems ◽  
Space Time ◽  
Semilinear Parabolic Systems ◽  
Semilinear Parabolic

scholarly journals Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sun-Hye Park
Keyword(s):  
Time Delay ◽  
Global Existence ◽  
Wave Equations ◽  
Blow Up ◽  
Logarithmic Sobolev Inequality ◽  
Decay Rates ◽  
Infinite Time ◽  
Global Existence Of Solutions ◽  
Frictional Damping ◽  
T Tau

AbstractIn this paper, we study the wave equation with frictional damping, time delay in the velocity, and logarithmic source of the form $$ u_{tt}(x,t) - \Delta u (x,t) + \alpha u_{t} (x,t) + \beta u_{t} (x, t- \tau ) = u(x,t) \ln \bigl\vert u(x,t) \bigr\vert ^{\gamma } . $$ u t t ( x , t ) − Δ u ( x , t ) + α u t ( x , t ) + β u t ( x , t − τ ) = u ( x , t ) ln | u ( x , t ) | γ . There is much literature on wave equations with a polynomial nonlinear source, but not much on the equations with logarithmic source. We show the local and global existence of solutions using Faedo–Galerkin’s method and the logarithmic Sobolev inequality. And then we investigate the decay rates and infinite time blow-up for the solutions through the potential well and perturbed energy methods.

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