Publisher： Academic Press
ISSN： 0022-247X
Source： Journal of Mathematical Analysis and Applications, Vol.203, Iss.3, 1996-11, pp. : 812-827
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Abstract
Of concern is the following totally nonlinear parabolic equation, as well as its higher space dimensional analogue eqalign{u_t(x,t)&=beta(phi(x,u_x)u_{xx}+f(x,u,u_x)),qquad (x,t)in(0,1)times(0,infty)cr u_x(j,t)&in(-1)^jbeta_j(u(j,t)),qquad j=0,1cr u(x,0)&=u_0(x).cr} Here beta 0 and beta 1 are maximal monotone graphs in R x R , and beta( t ) or beta'( t ) might equal zero for some t , at which the equation is not uniformly parabolic. It is shown by the method of lines and nonlinear operator semigroup theory that the equation has a unique global solution.
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