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BLOW UP OF SOLUTIONS TO A SEMILINEAR PARABOLIC SYSTEM WITH NONLOCAL SOURCE AND NONLOCAL BOUNDARY
Peng, Congming,Yang, Zuodong The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper we investigate the blow up properties of the positive solutions to a semi linear parabolic system with coupled nonlocal sources $u_t={\Delta}u+k_1{\int}_{\Omega}u^{\alpha}(y,t)v^p(y,t)dy,\;v_t={\Delta}_v+k_2{\int}_{\Omega}u^q(y,t)v^{\beta}(y,t)dy$ with non local Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set.
Blow up of solutions to a semilinear parabolic system with nonlocal source and nonlocal boundary
Congming Peng,Zuodong Yang 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper we investigate the blow up properties of the positive solutions to a semilinear parabolic system with coupled nonlocal sources ut = Δu+k1 ∫Ωuα(y, t)vp(y, t)dy, vt = Δv+k2∫Ω uq (y, t)vβ(y, t)dy with nonlocal Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set.. In this paper we investigate the blow up properties of the positive solutions to a semilinear parabolic system with coupled nonlocal sources ut = Δu+k1 ∫Ωuα(y, t)vp(y, t)dy, vt = Δv+k2∫Ω uq (y, t)vβ(y, t)dy with nonlocal Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set..