Blow-up and lifespan of solutions to a nonlocal parabolic equation at arbitrary initial energy level

2018 ◽  
Vol 78 ◽  
pp. 118-125 ◽  
Author(s):  
Jun Zhou
Keyword(s):  
Parabolic Equation ◽  
Energy Level ◽  
Blow Up ◽  
Initial Energy ◽  
Nonlocal Parabolic Equation

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 Large Solutions for Semilinear Parabolic Equations Involving Some Special Classes of Nonlinearities

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Constantin P. Niculescu ◽  
Ionel Rovenţa
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Blow Up ◽  
Neumann Boundary ◽  
Semilinear Parabolic Equations ◽  
New Class ◽  
Large Solutions ◽  
Nonlocal Parabolic Equation ◽  
Work Done ◽  
Semilinear Parabolic

We consider a new class of nonlinearities for which a nonlocal parabolic equation with Neumann boundary conditions has finite time blow-up solutions. Our approach is inspired by previous work done by Jazar and Kiwan (2008) and El Soufi et al. (2007).

Blow-up for a nonlocal parabolic equation

2009 ◽  
Vol 71 (7-8) ◽  
pp. 3551-3562 ◽  
Author(s):  
Fei Liang ◽  
Yuxiang Li
Keyword(s):  
Parabolic Equation ◽  
Blow Up ◽  
Nonlocal Parabolic Equation

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.

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