Global Attractor for Doubly Nonlinear Parabolic Equation
Global Attractor for Doubly Nonlinear Parabolic Equation
Our aim in this paper is to study the long-time behavior for a class of doubly nonlinear parabolic equations. First we show that the problem has a unique solution. Then we prove that the semigroup corresponding to the problem is norm-to-weak continuous in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>q</mml:mi></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msubsup><mml:mi>H</mml:mi><mml:mn>0</mml:mn><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:math> …