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- W2994594826 abstract "In this work, we investigate the qualitative properties as uniqueness, regularity and stabilization of the weak solution to the nonlinear parabolic problem involving general $p(x)$-homogeneous operators: begin{equation*} left{ begin{alignedat}{2} {} frac{q}{2q-1}partial_t(u^{2q-1}) -nabla., a(x, nabla u) & {}= f(x,u) + h(t,x) u^{q-1} && quadmbox{ in } , (0,T) times Omega; u & {}> 0 && quadmbox{ in }, (0,T) times Omega ; u & {}= 0 && quadmbox{ on }, (0,T) times partialOmega; u(0,.)&{}= u_0 && quad mbox{in}, Omega. end{alignedat} right. end{equation*} Thanks to the Picone's identity obtained in [10], we prove new results about comparison principles which yield a priori estimates, positivity and uniqueness of weak solutions." @default.
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- W2994594826 date "2019-12-05" @default.
- W2994594826 modified "2023-09-27" @default.
- W2994594826 title "Doubly nonlinear equation involving $p(x)$-homogeneous operators: local existence, uniqueness and global behaviour" @default.
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