【摘 要】
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In this paper we consider the well-posedness and the asymptotic behavior of solutions to the following parabolic-hyperbolic phase field system { Xt-△X + X3
【机 构】
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SchoolofMathematicalSciences,FudanUniversity,Shanghai,China
【出 处】
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International Conference on Nonlinear PDEs and Their Applica
论文部分内容阅读
In this paper we consider the well-posedness and the asymptotic behavior of solutions to the following parabolic-hyperbolic phase field system { Xt-△X + X3-X-θ =O,θt + Xt + divq =O,(1)qt + q + ▽θ =0,in Ω × (0,+∞) subject to the homogeneous Neumann boundary condition for x(δ)nX =O,on Γ×(0,+∞),(2)and no-heat flux boundary condition for q q·n=0,on Γ×(0,+∞),(3)and the initial conditions x(0)=x0,θ(0)=θ0,q(0)=q0,inΩ,(4) where Ω (U) R3 is a bounded domian with a smooth boundary (T) and n is the outward normal direction to the boundary.
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