Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation
Copyright policy )Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation
We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the formd/dt𝒜u+ℬu∋ftinV′,t∈0, T, whereVis a real reflexive Banach space,𝒜andℬare maximal monotone operators (possibly multivalued) fromVto its dualV′. In view of some practical applications, we assume that𝒜andℬare subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of𝒜and the coerciveness ofℬ. As an application, we give the existence for a nonlinear degenerate parabolic equation.
- Tsinghua University China (People's Republic of)
Abstract parabolic equations, Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions), Equations involving nonlinear operators (general), QA1-939, Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations, Monotone operators and generalizations, Mathematics
Abstract parabolic equations, Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions), Equations involving nonlinear operators (general), QA1-939, Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations, Monotone operators and generalizations, Mathematics
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