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Approximate solutions for multivalued quasilinear elliptic differential equations. (Chinese. English summary) Zbl 0898.35038

Summary: As a model for nonlinear multivalued elliptic differential equations, a boundary value problem for a multivalued quasilinear elliptic differential equation of the form \(-\Delta u\in f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial \Omega\) is discussed. The existence and convergence of approximate solutions are proved. A numerical realization is given for some examples.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35R70 PDEs with multivalued right-hand sides
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35A35 Theoretical approximation in context of PDEs
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