Geodesic
Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 431-443.

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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.
Classification : 35B40, 35K35, 35K55, 35K60
Keywords: nonlinear parabolic equation; initial boundary value problem; classical global solutions 
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     author = {Chen, Guowang},
     title = {Classical global solutions of the initial boundary value problems  for a class of nonlinear parabolic equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {431--443},
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     zbl = {0808.35049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1994__35_3_a1/}
}
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Chen, Guowang. Classical global solutions of the initial boundary value problems  for a class of nonlinear parabolic equations. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 431-443. http://geodesic.mathdoc.fr/item/CMUC_1994__35_3_a1/