When something bad or painful abates, it becomes less strong or severe.

You allay someone’s fear or concern by making them feel less afraid or worried.

If you alleviate pain or suffering, you make it less intense or severe.

When you ameliorate a bad condition or situation, you make it less harmful in some way, thereby improving it.

An anodyne is a medicine that soothes or relieves pain.

To augment something is to increase its value or effectiveness by adding something to it.

If you describe someone as benign, they are kind, gentle, and harmless.

If you condole with someone, you express sympathy or sorrow, usually on the death of someone dear.

If there are extenuating circumstances in a questionable situation, you feel that it was reasonable for someone to break the usual rules; therefore, you partly excuse and sympathize with their wrongdoing.

To foment is to encourage people to protest, fight, or cause trouble and violent opposition to something that is viewed by some as undesirable.

An incendiary device causes objects to catch on fire; incendiary comments can cause riots to flare up.

When you incite someone to do something, you encourage, urge, or highly persuade them to do it.

If someone has an insatiable desire for something she always wants more of it and never feels that she has enough.

When you instigate something, you start it or stir it up, usually for the purpose of causing trouble of some kind.

If you mitigate something that causes harm, you reduce the harmful or painful effects of it.

If you mollify someone, you say or do something to make that person feel less angry or upset.

A palliative action makes a bad situation seem better; nevertheless, it does not actually solve the problem.

A panacea is something that people think will solve all problems and make everything better.

To propitiate another is to calm or soothe them; it is often giving someone what they want so that everyone is happy.

To quell something is to stamp out, quiet, or overcome it.

If you describe a person’s behavior as rapacious, you disapprove of them because they always want more money, goods, or possessions than they really need.

If you are ravenous, you are extremely hungry.

If something, such as food or drink, satiates you, it satisfies your need or desire so completely that you often feel that you have had too much.

If something—such as power, influence, or feeling—wanes, it gradually becomes weaker or less important, often so much so that it eventually disappears.

When something whets your appetite, it increases your desire for it, especially by giving you a little idea or pleasing hint of what it is like.