Periodic solutions for double degenerate quasilinear parabolic equations
This paper deals with the existence of periodic solutions for the following double degenerate quasilinear parabolic equations of the type \[ \begin{aligned} \frac{\partial(b(x)u)}{\partial t}-\sum_{i=1}^ND_iA_i(x,t,u,Du)+A_0(x,t,u)=f(x,t)&\quad\text{in }Q:=\Omega\times (0,T),\\ b(x)u(x,0)=b(x)u(x,T)&\quad\text{in }\Omega, \end{aligned} \tag{1} \] on the space \(X=L^2(0,T;V)\), where \(V=W^{1,2}_0(v,\Omega)\) is a weighted Sobolev space. The degeneration is determined by a scalar function \(b(x)\) and a vector function \(v(x)=(v_1(x),\cdots,v_N(x))\) with positive components \(v_i(x)\) in \(\Omega\) satisfying certain integrability assumptions. Under some appropriate hypothesis, the author proves the existence of periodic solution for problem (1).
scientific article; zbMATH DE number 1836643