Parabolic Singular Problems With KPZ‐Nonlinearities and Nonlocal Conditions

Mixed problems in cylindrical domains with integral‐type nonlocal conditions on the lateral part of the boundary are investigated for singular quasilinear parabolic equations with nonlinearities of the Kardar–Parisi–Zhang type, arising in various applications. Depending on the relations between the three key parameters (the coefficient at the singular term of the equation, the power of the semilinear term of the equation, and the power at the nonlocal condition), the properties of the weight function at the nonlocal condition, and the geometric properties of the cylinder base, theorems of existence or nonexistence of solutions are proved.