How can one deal with a husband who is characterized by lying and deceit, who abandons his wife and mistreats her, knowing that he has fallen short in his marital duties, creates problems, claims to be traveling while he is residing in the same country, and refuses to communicate with his wife?

Among the rights of a wife over her husband are good companionship and that he should not be absent from her for more than six months, except with her permission. The husband's treatment of his wife, as mentioned in the question, constitutes a great neglect of her right and is not an act of good companionship. The wife is advised to be patient, to make frequent supplications, and to continue advising her husband and reminding him of Allah. If the husband does not repent and give his wife her right, she is entitled to seek divorce to دفعاً للضرر (ward off harm). If he does not respond, she should refer the matter to the شرعي (Sharia) court. She may also choose to be patient and continue advising him.