A Study On Inital-Boundary Value Problem Of The Nonlinear Thermoelastic Coupled Partial Differential Equations

Recently, due to the development of mathematic and promotion of physicsand other mechanics, the study of partial differential equation have been becomeimportant subject in the mathematical research field. This thesis makes researchabout the problem of nonlinear thermoelastic coupled beam which possessesspecified initial boundary condition, namely, the following coupled equationProfiting the method of Galerkin, we give the proof of weak solution, strongsolution and the existence of classical solution under the initial conditionand boundary conditionAt the same time, profiting the method of Galerkin, we give the proof of theexistence of weak solution and strong solution under the same initial condition andnonlinear boundary condition kθ⁽¹⁾(1,t)=-βθ(1,t), u⁽²⁾(1,t)=0 u(0,t)=u⁽¹⁾(0,t)=0,θ⁽¹⁾(0,t)=0...