# Article

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Keywords:
nonlinear parabolic equation; initial boundary value problem; classical global solutions
Summary:
The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation $$u_t=-A(t)u_{x^4}+B(t)u_{x^2}+g(u)_{x^2}+f(u)_{x}+h(u_{x})_{x}+G(u)$$ with the initial boundary value conditions $$u(-\ell ,t)=u(\ell ,t)=0,\quad u_{x^2}(-\ell ,t)=u_{x^2}(\ell ,t)=0,\quad u(x,0)=\varphi (x),$$ or with the initial boundary value conditions $$u_{x}(-\ell ,t)=u_{x}(\ell ,t)=0,\quad u_{x^3}(-\ell ,t)=u_{x^3}(\ell ,t)=0,\quad u(x,0)=\varphi (x),$$ are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.
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