On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model
М. О. Корпусов, A. Yu. Perlov, Alexander V. Timoshenko, Р. С. Шафир
Abstract
Abstract In this paper, we propose a system of nonlinear equations for the electric field potential and temperature, which describes the process of heating the semiconductor elements of an electrical board followed by thermal breakdown. For this system of equations, we prove the existence of a classical solution that is not extendable in time and also obtain sufficient conditions for the solution to blow up in finite time.
Topics & Concepts
MathematicsNonlinear systemThermalMathematical analysisApplied mathematicsThermodynamicsPhysicsQuantum mechanicsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential EquationsNumerical methods in inverse problems