1. Take the backup of web application content database on SharePoint 2010 from sql server using Sql Server Management Studio
2. On SharePoint 2013 create new web application. Pay attention that on SharePoint 2010 your application probably has classic-mode authentication, while on SharePoint 2013 the default is claims-based authentication. To create classic-mode web application in a SharePoint 2013, execute this command in PowerShell:
New-SPWebApplication –name "<WebAppName>"
–Port <PortNumber>
–ApplicationPool "<AppPoolName>"
–ApplicationPoolAccount (Get-SPManagedAccount "<Domain>\<AccountName>")
To use an existing application pool, provide only application pool name, without account.
3. Deploy all required farm solutions to the new web application
4. Remove content database from newly created web application in Central Administration > Manage Content Databases
5. Detach or delete the content database using Sql Server Management Studio
6. Now restore the backuped database.
7. Attach the restored content database to new web application using PowerShell:
Mount-SPContentDatabase -Name <DatabaseName> -DatabaseServer <DBServerName> -WebApplication <WebAppURL>
