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The Partial Second Boundary Value Problem of an 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… Click to show full abstract

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 Γ2Ω, then the second boundary value condition is imposed on the remaining part ΩΓ2. The uniqueness of weak solution can be proved without the boundary value condition on Γ2.

Keywords: mml msub; mrow mml; mml; mml mml; mml mrow

Journal Title: Journal of Function Spaces
Year Published: 2019

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