Abstract:
The first boundary-value problem for the equation
β(u)∂u∂t−n∑i=1DiAi(t,x,u,Du)+A0(t,x,u,Du)=0
is considered in a bounded subdomain of n. The function β(u) is assumed to be continuous and satisfy the following growth conditions:
c|u|r−2⩽β(u)⩽C(|u|r−2+1),r⩾2.
The other coefficients satisfy the standard conditions of the theory of monotone operators. An existence theorem for a global weak solution is proved.
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