I write a web site. On this site, there will be a lot a user connected at a time? I use Hibernate OR mapping layer, and tomcat as Server.

What is the best way to manage such a lot of connections at a time ? Is there a pattern to resolve it? If yes, which is this pattern and how it works.

Thanks.

There are a lot good ways, but I think cache is the best way.

BTW "user count" is not a good metric for web application ( "a lot of users" says nothing for me), It must be better to use "pages per sec." to test availability (You must not overuse http session for things like resource management).

Use connection pooling and stateless design.

Connection polling allow you to limit the number of connection into your DB by taking then through a limited pool (10 cnx for example).
See the 2.4 section of hibernate reference guide for more information on connection pooling and hibernate.
See http://jakarta.apache.org/commons/dbcp/ for an alternative implementation

Stateless design
Do not store user specific data into Servlet Sessions (or limit this amount).
Do not let opened session into user servlet session: this will keep the DB connection opened.

You can find more information by googleing those terms. These are very general design strategies (not specific to hibernate)