非线性非局部边界条件的半线性耦合抛物型方程组

Abstract

Abstract:

This paper considers a semilinear parabolic system u_it =Δu_i+c_i(x,t)u_i+1^p_i for (x,t)∈ Ω × (0,∞) subject to weighted nonlocal Dirichlet boundary conditions ∫_Ωψ_i(x,y,t)u_i^l_i (y,t)dy and nonnegative initial data. Some criteria on this problem which determine whether the solutions blow up in a finite time or the solutions exist for all time are given. These results show that the weight functions c_i(x,t), ψ_i(x,y,t) and the size of exponents p_i, l_i play substantial roles in determining whether the solutions are global or blow-up.

Key words: Parabolic system, Nonlocal boundary condition, Weight function, Global solution, Blow-up

CLC Number:

O175.2

Ling Zhengqiu, Qin Siqian. Coupled Semilinear Parabolic System with Nonlinear Nonlocal Boundary Condition[J].Acta mathematica scientia,Series A, 2015, 35(2): 234-244.

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References

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Coupled Semilinear Parabolic System with Nonlinear Nonlocal Boundary Condition

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