Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source

2022 ◽  
Vol 64 ◽  
pp. 103449
Author(s):  
Bingchen Liu ◽  
Min Zhang ◽  
Fengjie Li
Keyword(s):  
Parabolic Equation ◽  
Variable Exponents

scholarly journals The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Huashui Zhan
Keyword(s):  
Weak Solution ◽  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Variable Exponents ◽  
Boundary Value Condition ◽  
Anisotropic Parabolic Equation

Consider an anisotropic parabolic equation with the variable exponents vt=∑i=1n(bi(x,t)vxipi(x)-2vxi)xi+f(v,x,t), where bi(x,t)∈C1(QT¯), pi(x)∈C1(Ω¯), pi(x)>1, bi(x,t)≥0, f(v,x,t)≥0. If {bi(x,t)} is degenerate on Γ2⊂∂Ω, then the second boundary value condition is imposed on the remaining part ∂Ω∖Γ2. The uniqueness of weak solution can be proved without the boundary value condition on Γ2.

Blow up in a semilinear pseudo-parabolic equation with variable exponents

2019 ◽  
Vol 65 (2) ◽  
pp. 311-326 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Ala A. Talahmeh
Keyword(s):  
Parabolic Equation ◽  
Blow Up ◽  
Variable Exponents

scholarly journals On an Anisotropic Parabolic Equation on the Domain with a Disjoint Boundary

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Huashui Zhan
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Boundary Value ◽  
Variable Exponents ◽  
Boundary Value Condition ◽  
Partial Boundary Value Condition ◽  
Anisotropic Parabolic Equation ◽  
The Stability

Consider the anisotropic parabolic equation with the variable exponentsvt=∑i=1n(bi(x)vxiqix-2vxi)xi,wherebi(x),qi(x)∈C1(Ω¯),qi(x)>1, andbi(x)≥0. If{bi(x)}is not degenerate onΣp⊂∂Ω, a part of the boundary, but is degenerate on the remained part∂Ω∖Σp, then the boundary value condition is imposed onΣp, but there is no boundary value condition required on∂Ω∖Σp. The stability of the weak solutions can be proved based on the partial boundary value conditionvx∈Σp=0.

scholarly journals Blow-up phenomena for a pseudo-parabolic equation with variable exponents

2017 ◽  
Vol 64 ◽  
pp. 67-73 ◽  
Author(s):  
Huafei Di ◽  
Yadong Shang ◽  
Xiaoming Peng
Keyword(s):  
Parabolic Equation ◽  
Blow Up ◽  
Variable Exponents
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