Mysql – MariaDB doesn’t start after upgrade from MySQL 5.7

I installed MariaDB server, my MySQL got removed automatically and I tried to get it running using sudo service mysql start, which caused the following error message:

    Job for mariadb.service failed because a timeout was exceeded.
    See "systemctl status mariadb.service" and "journalctl -xe" for details.

Systemctl status mariadb.service answered me:

● mariadb.service - MariaDB database server
   Loaded: loaded (/lib/systemd/system/mariadb.service; enabled; vendor preset: enabled)
   Active: failed (Result: timeout) since Thu 2018-08-02 22:28:04 CEST; 10min ago
  Process: 10343 ExecStart=/usr/sbin/mysqld $MYSQLD_OPTS $_WSREP_NEW_CLUSTER $_WSREP_START_POSITION (code=exited, status=0/SUCCESS)
  Process: 10256 ExecStartPre=/bin/sh -c [ ! -e /usr/bin/galera_recovery ] && VAR= ||   VAR=`/usr/bin/galera_recovery`; [ $? -eq 0 ]   && systemctl set-environment _WSREP_START_POSITION=$VAR || exit 1 (co
  Process: 10252 ExecStartPre=/bin/sh -c systemctl unset-environment _WSREP_START_POSITION (code=exited, status=0/SUCCESS)
  Process: 10247 ExecStartPre=/usr/bin/install -m 755 -o mysql -g root -d /var/run/mysqld (code=exited, status=0/SUCCESS)
 Main PID: 10343 (code=exited, status=0/SUCCESS)

Aug 02 22:26:31 example.com systemd[1]: Starting MariaDB database server...
Aug 02 22:26:32 example.com mysqld[10343]: 2018-08-02 22:26:32 140165196823680 [Note] /usr/sbin/mysqld (mysqld 10.1.29-MariaDB-6) starting as process 10343 ...
Aug 02 22:28:02 example.com systemd[1]: mariadb.service: Start operation timed out. Terminating.
Aug 02 22:28:04 example.com systemd[1]: mariadb.service: Failed with result 'timeout'.
Aug 02 22:28:04 example.com systemd[1]: Failed to start MariaDB database server.

Journalctl on the other hand specified it more detailled as a authentication error, as far as I can read it out:

$ journalctl -xe
Aug 02 22:16:51 example.com sudo[10011]: pam_unix(sudo:session): session opened for user root by nekura(uid=0)
Aug 02 22:16:53 example.com systemd[1]: Starting MariaDB database server...
-- Subject: Unit mariadb.service has begun start-up
-- Defined-By: systemd
-- Support: http://www.ubuntu.com/support
-- 
-- Unit mariadb.service has begun starting up.
Aug 02 22:16:53 example.com mysqld[10139]: 2018-08-02 22:16:53 139725684759680 [Note] /usr/sbin/mysqld (mysqld 10.1.29-MariaDB-6) starting as process 10139 ...
Aug 02 22:16:53 example.com audit[10139]: AVC apparmor="DENIED" operation="sendmsg" info="Failed name lookup - disconnected path" error=-13 profile="/usr/sbin/mysqld" name="run/systemd/notify" pid=
Aug 02 22:16:53 example.com kernel: audit: type=1400 audit(1533241013.968:40): apparmor="DENIED" operation="sendmsg" info="Failed name lookup - disconnected path" error=-13 profile="/usr/sbin/mysql
Aug 02 22:16:56 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:17:01 example.com CRON[10167]: pam_unix(cron:session): session opened for user root by (uid=0)
Aug 02 22:17:01 example.com CRON[10168]: (root) CMD (   cd / && run-parts --report /etc/cron.hourly)
Aug 02 22:17:01 example.com CRON[10167]: pam_unix(cron:session): session closed for user root
Aug 02 22:17:04 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:17:18 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:17:39 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:17:47 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:17:52 example.com sshd[10170]: pam_unix(sshd:auth): authentication failure; logname= uid=0 euid=0 tty=ssh ruser= rhost=182.100.67.106  user=root
Aug 02 22:17:55 example.com sshd[10170]: Failed password for root from 182.100.67.106 port 56800 ssh2
Aug 02 22:17:58 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:18:06 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:18:08 example.com sshd[10170]: Failed password for root from 182.100.67.106 port 56800 ssh2
Aug 02 22:18:15 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:18:16 example.com sshd[10170]: Failed password for root from 182.100.67.106 port 56800 ssh2
Aug 02 22:18:16 example.com sshd[10170]: Received disconnect from 182.100.67.106 port 56800:11:  [preauth]
Aug 02 22:18:16 example.com sshd[10170]: Disconnected from authenticating user root 182.100.67.106 port 56800 [preauth]
Aug 02 22:18:16 example.com sshd[10170]: PAM 2 more authentication failures; logname= uid=0 euid=0 tty=ssh ruser= rhost=182.100.67.106  user=root
Aug 02 22:18:23 example.com systemd[1]: mariadb.service: Start operation timed out. Terminating.
Aug 02 22:18:23 example.com kernel: audit: type=1400 audit(1533241103.679:41): apparmor="DENIED" operation="sendmsg" info="Failed name lookup - disconnected path" error=-13 profile="/usr/sbin/mysql
Aug 02 22:18:23 example.com audit[10139]: AVC apparmor="DENIED" operation="sendmsg" info="Failed name lookup - disconnected path" error=-13 profile="/usr/sbin/mysqld" name="run/systemd/notify" pid=
Aug 02 22:18:25 example.com audit[10139]: AVC apparmor="DENIED" operation="sendmsg" info="Failed name lookup - disconnected path" error=-13 profile="/usr/sbin/mysqld" name="run/systemd/notify" pid=
Aug 02 22:18:25 example.com kernel: audit: type=1400 audit(1533241105.719:42): apparmor="DENIED" operation="sendmsg" info="Failed name lookup - disconnected path" error=-13 profile="/usr/sbin/mysql
Aug 02 22:18:25 example.com systemd[1]: mariadb.service: Failed with result 'timeout'.
Aug 02 22:18:25 example.com sudo[10011]: pam_unix(sudo:session): session closed for user root
Aug 02 22:18:25 example.com systemd[1]: Failed to start MariaDB database server.
-- Subject: Unit mariadb.service has failed
-- Defined-By: systemd
-- Support: http://www.ubuntu.com/support
-- 
-- Unit mariadb.service has failed.
-- 
-- The result is RESULT.
Aug 02 22:18:25 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:18:44 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:18:47 example.com sshd[10183]: pam_unix(sshd:auth): authentication failure; logname= uid=0 euid=0 tty=ssh ruser= rhost=182.100.67.106  user=root
Aug 02 22:18:49 example.com sshd[10183]: Failed password for root from 182.100.67.106 port 39521 ssh2
Aug 02 22:18:51 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:19:11 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:19:28 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:19:38 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:19:48 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:19:59 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)
Aug 02 22:20:09 example.com dhclient[943]: DHCPREQUEST of 123.123.123.123 on ens3 to 255.255.255.255 port 67 (xid=0x5ab749b3)

I also took a look into the error log, which listed only some notes:

2018-08-02 22:26:32 140165196823680 [Note] InnoDB: innodb_empty_free_list_algorithm has been changed to legacy because of small buffer pool size. In order to use backoff, increase buffer pool at least up to 20MB.

2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Using mutexes to ref count buffer pool pages
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: The InnoDB memory heap is disabled
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Mutexes and rw_locks use GCC atomic builtins
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: GCC builtin __atomic_thread_fence() is used for memory barrier
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Compressed tables use zlib 1.2.11
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Using Linux native AIO
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Using SSE crc32 instructions
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Initializing buffer pool, size = 128.0M
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Completed initialization of buffer pool
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Highest supported file format is Barracuda.
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: 128 rollback segment(s) are active.
2018-08-02 22:26:32 140165196823680 [Note] InnoDB: Waiting for purge to start
2018-08-02 22:26:32 140165196823680 [Note] InnoDB:  Percona XtraDB (http://www.percona.com) 5.6.36-82.2 started; log sequence number 1616757
2018-08-02 22:26:32 140165196823680 [Note] Plugin 'FEEDBACK' is disabled.
2018-08-02 22:26:32 140164575749888 [Note] InnoDB: Dumping buffer pool(s) not yet started
2018-08-02 22:26:32 140165196823680 [Note] Server socket created on IP: '127.0.0.1'.
2018-08-02 22:26:32 140165196823680 [Note] /usr/sbin/mysqld: ready for connections.
Version: '10.1.29-MariaDB-6'  socket: '/var/run/mysqld/mysqld.sock'  port: 3306  Ubuntu 18.04
2018-08-02 22:28:02 140165196183296 [Note] /usr/sbin/mysqld: Normal shutdown

I already ran mysql_secure_installation, but without success. How can I fix the server installation?