Sharif Digital Repository

This thesis is devoted to prove the existance of solution and structure of solu­ tion for some partial differential equations by using some modern topological and variational thechniques. Taking direction from the literature, this thesis is interested in existence, uniqueness, blow-up in finite time for some evolution equations, multiplicity and radial solution for certain elliptic partial differential equations.-Employing Fibrering, Galerkins, Mountain Pass-Lemma and lions com­ pactness Lemma are sharp in this thesis to prove the exsistence and multiplicity of solutions and overcome lack of compactness in some cases  

We discuss, in the setting of UMD Banach spaces E, existence, uniqueness and the continuous dependence on the data A, F, G and of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t;X(t))]dt + G(t;X(t))dWH(t); t 2 [0; T]; X(0) = ; Where A generates an analytic C0-semigroup on a UMD Banach space E and WH is a cylindrical Brownian motion with values in a Hilbert space H. We can see that if the mappings F : [0; T] E ! E and G : [0; T] E ! L(H;E) satisfy suitable Lipschitz conditions and is F0-measurable and bounded, then this problem has a unique mild solution.And We arw going to review continuous dependence of the solutions... 

In the presented dissertation an analytical model is developed for the air gap flux density and the cogging torque in the axial flux surface-mounted PM machines. The slotting effect is taken into account in the magnetic flux distribution.The model is derived from solving the 2D Poisson' equation in the slotted air gap. To simplify the solution process, the concept of the uniqueness theorem is used to replace the slotted air gap by a slotless one and some surface current distribution. In addition, the separation of variables method is applied to the analytical solution of the Poisson equation. However, the proposed 2D analytical model is developed for the quasi 3D model by the well-known...