Quadratic Poisson's Equation

Quadratic Poisson's Equation is a type of mathematical problem that involves finding a function whose second derivatives relate to the function's square. Essentially, it extends the classical Poisson equation, which models phenomena like heat distribution or gravitational potential, by including a quadratic term. This makes the equation nonlinear, meaning its solutions can be more complex. It’s useful in physics and engineering when systems involve interactions that depend on the square of the quantity, such as certain electromagnetic or fluid flow problems. Solving it helps understand how quantities evolve or distribute in more complex, real-world situations where relationships are not purely linear.