An existence theorem for an implicit nonlinear evolution equation (Q1070513)
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scientific article; zbMATH DE number 3935837
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence theorem for an implicit nonlinear evolution equation |
scientific article; zbMATH DE number 3935837 |
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An existence theorem for an implicit nonlinear evolution equation (English)
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1984
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We prove the existence of a solution for a nonlinear evolution equation of the form: \((d/dt)B(u(t))+A(t,u(t))\ni f(t)\), where A and B are nonlinear operators, possibly multivalued. The proof is based on implicit discretization in time and passing to the limit as the time step goes to zero. An application to a Stefan problem, arising from the solidification of a metal in a mould, is given.
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multivalued operator
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nonlinear evolution equation
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implicit discretization in time
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Stefan problem
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