Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations
Chen, Guo Wang
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 431-443 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1994-01-01
Classification:  35B40,  35K35,  35K55,  35K60 
@article{118684,
     author = {Guo Wang Chen},
     title = {Classical global solutions of the initial boundary value problems  for a class of nonlinear parabolic equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {431-443},
     zbl = {0808.35049},
     mrnumber = {1307271},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118684}
}

Chen, Guo Wang. Classical global solutions of the initial boundary value problems  for a class of nonlinear parabolic equations. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 431-443. http://gdmltest.u-ga.fr/item/118684/

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