Docker Compose - простой пример - mysql + tomcat

# vi docker-compose.yml

version: "2"
 services:
  db:
    container_name: dbserver
    environment:
      - MYSQL_ROOT_PASSWORD=test1
      - MYSQL_DATABASE=test1
      - MYSQL_USER=test1
      - MYSQL_PASSWORD=test1
    image: "mysql:latest"
    ports:
      - "3306:3306"
  tomcat:
    container_name: appserver
    depends_on:
      - db
    image: "tomcat:latest"
    ports:
      - "8080:80"

Обязательно проверить через валидатор и запуск:

# docker-compose up -d