**Core Concept**
The patient's presentation of epigastric pain radiating to the back, relieved by food intake, and a history of recurrent duodenal ulcers, suggests a diagnosis related to peptic ulcer disease (PUD). The key concept here is the pathophysiology of duodenal ulcers, which involves gastric acid secretion and mucosal defense mechanisms.

**Why the Correct Answer is Right**
The patient's symptoms are consistent with a diagnosis of **Zollinger-Ellison Syndrome (ZES)**. ZES is a rare condition characterized by excessive gastric acid secretion due to a gastrin-secreting tumor, leading to recurrent peptic ulcers. The elevated gastrin levels stimulate the parietal cells in the stomach to secrete more acid, causing ulcers. The patient's history of perforated duodenal ulcers and response to proton pump inhibitors (PPIs) also supports this diagnosis.

**Why Each Wrong Option is Incorrect**
**Option A:** **Gastroesophageal Reflux Disease (GERD)** is unlikely, as the patient's symptoms are not typical of acid reflux, and the pain is relieved by food intake.

**Option B:** **Crohn's Disease** is a type of inflammatory bowel disease that can cause abdominal pain, but it is not typically associated with epigastric pain radiating to the back or a history of recurrent peptic ulcers.

**Option C:** **Pancreatitis** can cause epigastric pain radiating to the back, but it is usually associated with other symptoms such as fever, nausea, and vomiting, and is not typically relieved by food intake.

**Clinical Pearl / High-Yield Fact**
Zollinger-Ellison Syndrome is a rare but important diagnosis to consider in patients with recurrent peptic ulcers, especially those with a history of perforation or failure to respond to standard treatments.

**Correct Answer: C. Pancreatitis.**