scholarly journals Anomalous pseudo-parabolic Kirchhoff-type dynamical model

2021 ◽  
Vol 11 (1) ◽  
pp. 503-534
Author(s):  
Xiaoqiang Dai ◽  
Jiangbo Han ◽  
Qiang Lin ◽  
Xueteng Tian
Keyword(s):  
Upper Bound ◽  
Dynamical Behavior ◽  
Dynamic Control ◽  
Local Existence ◽  
Initial Energy ◽  
Existence Of Solution ◽  
Dynamical Model ◽  
Time Behavior ◽  
Kirchhoff Type ◽  
Blowup Time

Abstract In this paper, we study an anomalous pseudo-parabolic Kirchhoff-type dynamical model aiming to reveal the control problem of the initial data on the dynamical behavior of the solution in dynamic control system. Firstly, the local existence of solution is obtained by employing the Contraction Mapping Principle. Then, we get the global existence of solution, long time behavior of global solution and blowup solution for J(u 0) ⩽ d, respectively. In particular, the lower and upper bound estimates of the blowup time are given for J(u 0)<d. Finally, we discuss the blowup of solution in finite time and also estimate an upper bound of the blowup time for high initial energy.

scholarly journals Qualitative properties of weak solution for pseudo-parabolic equation contain viscoelastis terns and associated with homogeneous Robin conditions

2020 ◽  
Author(s):  
Nhan Truong ◽  
Danh Pham ◽  
Dung Huynh ◽  
Tran Minh
Keyword(s):  
Parabolic Equation ◽  
Upper Bound ◽  
Blow Up ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Negative Energy ◽  
Initial Energy ◽  
Qualitative Properties ◽  
Standard Galerkin Method

In this paper, we consider initial boundary value problem of the generalized pseudo-parabolic equation contain viscoelastic terms and associated with Robin conditions. We establish firstly the local existence of solutions by standard Galerkin method. Then we prove blow-up results for solutions when the initial energy is negative or nonnegative but small enough or positive arbitrary high initial energy respectively. We also establish the lifespan for the equation via finding the upper bound and the lower bound for the blow-up times. For negative energy, we introduce a new method to prove blow-up results with sharper estimate for upper bound for the blow-up times. Finally, we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

scholarly journals Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuxuan Chen ◽  
Jiangbo Han
Keyword(s):  
Energy Level ◽  
Global Existence ◽  
Blow Up ◽  
Parabolic Systems ◽  
Initial Energy ◽  
Blowup Time ◽  
Positive Initial Energy ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Coupled Parabolic Systems

<p style='text-indent:20px;'>In this paper, we consider a class of finitely degenerate coupled parabolic systems. At high initial energy level <inline-formula><tex-math id="M1">\begin{document}$ J(u_{0})&gt;d $\end{document}</tex-math></inline-formula>, we present a new sufficient condition to describe the global existence and nonexistence of solutions for problem (1)-(4) respectively. Moreover, by applying the Levine's concavity method, we give some affirmative answers to finite time blow up of solutions at arbitrary positive initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_{0})&gt;0 $\end{document}</tex-math></inline-formula>, including the estimate of upper bound of blowup time.</p>

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

TIP INSTABILITY DURING CONFINED DIFFUSION-LIMITED GROWTH

1988 ◽  
Vol 02 (08) ◽  
pp. 945-951 ◽  
Author(s):  
DAVID A. KESSLER ◽  
HERBERT LEVINE
Keyword(s):  
Evolution Equations ◽  
Dynamical Behavior ◽  
Stable Steady State ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Limited Growth ◽  
Channel Geometry ◽  
Diffusion Limited ◽  
Long Time

We study diffusion-limited crystal growth in a two dimensional channel geometry. We demonstrate that although there exists a linearly stable steady-state finger solution of the pattern evolution equations, the true dynamical behavior can be controlled by a tip-widening instability. Possible scenarios for the long-time behavior of the system are presented.

scholarly journals THE DYNAMICS OF TACHYON FIELD WITH AN INVERSE SQUARE POTENTIAL IN LOOP QUANTUM COSMOLOGY

2013 ◽  
Vol 22 (06) ◽  
pp. 1350030 ◽  
Author(s):  
FEI HUANG ◽  
JIAN-YANG ZHU ◽  
KUI XIAO
Keyword(s):  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Loop Quantum Cosmology ◽  
Phase Plane Analysis ◽  
Late Time ◽  
Stable Node ◽  
Time Behavior ◽  
Tachyon Field ◽  
Plane Analysis ◽  
The Stability

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late-time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index 0 < γ < 2 is added and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy.

CHAOS AND DYNAMICS OF CYCLIC TRUCKING OF SIZE TWO

2005 ◽  
Vol 15 (12) ◽  
pp. 4065-4073 ◽  
Author(s):  
TAKASHI NAGATANI
Keyword(s):  
Delay Time ◽  
Arrival Time ◽  
Dynamical Behavior ◽  
Dynamical Model ◽  
Chaotic Motions ◽  
Time Headway ◽  
Time Variations ◽  
Loading Parameter ◽  
Varying Delay

We study dynamical behavior of a few trucks which shuttle between an origin and a destination repeatedly. One loads goods on to trucks at the origin and the truck unloads at the destination. We present the dynamical model for cyclic trucking. The model is described in terms of only one nonlinear map defined from the vector Ti(n), i = 1,2,…,N for N trucks where Ti(n) is the arrival time of truck i at the origin on trip n. The study is limited to the case of two trucks. We clarify the time variations of time headway and tour time for the truck schedule. The distinct dynamical states (the regular, periodic, and chaotic motions) are found by varying delay time T min and loading parameter Γ. It is shown that dynamical transitions occur among the regular, periodic and chaotic motions. In periodic and chaotic motions, the tour time of trucks fluctuates highly and the carrying goods vary the tour time accordingly.

Sign in / Sign up

Export Citation Format

Share Document