Sharif Digital Repository

In this thesis , we consider nonnegative (continuous) weak solutions of the porous medium equation with source , u_t-∆u^m=u^p, and p>m>1 .
Assume that, m>1 and 1< p/m u_t-∆u^m=u^p,xϵR^n ,tϵR
has no nontrivial, bounded radial solutions u≥0 .
In one space-dimensional, the conclusion of the result mentioned above remains true without the assumption of the radial symmetry. The proof is based on the intersection-comparison arguments , zero number argum- ents and a key step is to show the... 

Our problem is to evaluation state and form of a tracer passing through the vessel. Using this method, we can identify the effect of during used in some defected parts of body. This evaluation leads to in solving a Laplace equation with mixed boundary condition. Separating that problem, we reach to a collection of algebraic and linear equations. Solving this system, we approximate coefficients of the solution with a series the existence and uniqueness of and analytic solution has been proved using the Eigen functions finally, using numerical algorithms, we have interpreted the analytical solutions.
 

In this paper, the Hopfield neural network models have investigated. Also the similar model with time -varying delays and constant coefficients has considered and with establishing some criterions, existence solution and it's exponential stability of the solution is investigated. Moreover, some special conditions for exponential stability by impulses and exponential stability by periodic impulses are obtained  

In this thesis, we consider the motion of a stretched string coupled with a rigid body at one end and we study the existence of periodic solution when a periodic force acts on the body. In this hybrid system, there is a weak dissipation that characterizes. The main difficulty of the study is related to the weak dissipation which does not ensure a uniform decay rate of the energy. In this thesis, firstly, under the condition of 0 1 0 , we prove there exists a periodic solution. Then, we change the conditions on , Indeed, we restrict ourselves to solve the problem. In this case, under the condition of 0 2 0 , we show there is a periodic solution for rational periods. In the last part, by... 

The hepatitis delta virus (HDV) is a rarest form of viral hepatitis, but has the worst outcomes for patients.It is a subviral satellite dependent on coinfection with hepatitis B (HBV) to replicate within the host liver.To date, there has been little to no modeling effort for HDV. Deriving and analyzing such a mathematicalmodel poses difficulty as it requires the inclusion of (HBV). Here we begin with a well-studied HBV modelfrom the literature and expand it to incorporate HDV. We investigate two models, one with and one withoutinfected hepatocyte replication. Additionally, we consider treatment by the drug lamivudine. Comparison of model simulations with experimental results of lamivudine... 

prey and predator model occurs when the growth rate of species decline and increase the growth rate of other species. In the first chapter of this thesis review of basic concepts and theorems are important. In the second quarter, positive solutions in a heterogeneous system model release Bazykin with classic techniques to points most important of which is the case. In the third season, Stability and bifurcation system and predator prey Bazykin model with the function response Bdyngtn- De Angelis to equilibrium the points. In the fourth chapter in the normal form prey and predator system model Bazykin discuss  

This thesis is concerned with the Boussinesq-Burgers system which models the propagation of bores by combing the dissipation, Dispasion and nonlinearity . we establish the global existence and asymptotical behavior of classical solutions of the initial value and Dirichlet boundary problem of the Boussinesq-Burgers system with the help of a lyapunov functional and the technique of Moser itrtation. Particularly we show that the solution converges to the constant stationary solution as time tends to infinity. Furthermore if we have real domain or non-hemogenous boundary condition then we will arrive constant stationary solution as time tends to infinity  

this work devoted to the optimal control problem for an ecosystem composed of one predator and two competing preys, and our goal is to maximize the total density of the three populations. we first investigate the existence and uniqueness of the positive strong solution for the controlled system, and find an optimal solution under given initial conditions. then we establish the first order necessary optimality condition, and point out that the optimal control has a bang-bang form. moreover, the second order necessary and sufficient optimality conditions are established  

In this study, we will examine persistence of various kinds of seasonally forced epidemiological models and seasonally varying predator-prey models. The results of our study regarding persistence of the models will be shown via basic reproduction number. We will show that, in the framework of our study and under some conditions, persistence is obtained as long as the basic reproduction number is bigger than one. We will also prove that, in the framework of our study and under sufficient conditions, if the basic reproduction number is smaller than one, the species under discussion won’t survive in the predator-prey models, and the disease(s) would go extinct in the epidemiological... 

this thesis , we examine several types of neural networks , including the Hopfield and Cohen- Gro ssberg neural networks , which have discrete time delays in neuronal states and discrete time delays in the time derivative of neuronal states . The study of these Stabilities is mainly done by constructing Lyapunov function and by using it , the global asymptotic stability is studied . A comparison between these Stabilities will also be made and examples for the application of the results will be provided  

This thesis studies a haptotaxis system proposed as a model for oncolytic virotherapy , accounting for interaction between uninfected cancer cells , infected cancer cells , extracellular matrix (ECM) and oncolytic virus . In addition to random movement , both uninfected and infected tumor cells migrate haptotactically toward higher ECM densities; moreover , besides degrading the non-diffusible ECM upon contact the two cancer cell populations are subject to an infection-induced transition mechanism driven by virus particles which are released by infected cancer cells ,and which assault the uninfected part of the tumor .The main results assert global classical solvability in an associated... 

We study the Navier-Stokes equations with an extra Eddy viscosity term in the whole space . We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove that when the regularizing parameter goes to zero, the solution of the regularized system converges to a turbulent solution of the initial system. In the first chapter, we have dedicated the necessary preliminaries and then in the second chapter, we have introduced the types of solutions. The third chapter introduces the necessary tools and their properties, with the help of which in the next chapter we have been able to make estimates and obtain their extensions to prove... 

This dissertation is devoted to the mathematical theory of two-dimensional injection of incompressible, irrota-tional, and inviscid fluids issuing from two infinitely long nozzles into a free stream.. In general, there is a free interface with constant jump of the Bernoulli constant on it, which is different and more difficult than the previous related works. Physically, it is called the collision fluid. The main result in this paper is that for given two co-axis symmetric infinitely long nozzles, imposing the incoming mass fluxes in the two nozzles, there is a unique piecewise smooth fluid collision function such that its free interface arises from the collision of fluids. It is a... 

In this thesis, we consider a neutral predator–prey model with the Beddington–DeAngelis functional response and impulsive effect. Sufficient conditions are obtained for the existence of positive periodic solutions by a systematic qualitative analysis. Some known results in the literature are generalized  

In this thesis, we consider a system containing fluid equations, structure equations, and equations of these two materials’ common interface in three dimensions and on the regular domains. We suppose that the solid which is described by the Lamé system of linear elasticity, moves inside an incompressible viscous fluid in three dimensions, and the fluid obeys the incompressible Navier-Stokes equations in a time-dependent domain. At the fluid–solid interface, natural conditions are imposed, continuity of the velocities and of the Cauchy stress forces. The fluid and the solid are coupled through these conditions. By this interaction, the fluid deforms the boundary of the solid which in turn... 

Third order differential equations which describe pseudospherical surfaces are considered. The complete classification of a class of such equations is given. A linear problem with one or more parameters, also known as zero curvature representation, for which the equation is the integrability condition, is explicitly given. The classification provides five large families of differential equations. Third order nonlinear dispersive wave equations, such as the Camassa–Holm equation and Degasperis–Procesi equation are examples contained in the classification. Many other explicit examples are included  

We consider a system of nonlinear partial differential equations corresponding to a generalization of a mathematical model for geographical spreading of dengue disease. the mosquito population is divided into subpopulations: winged form (mature female mosquitoes) and aquatic form (comprising eggs, larvae and pupae); the human population is divided into the subpopulations:susceptible, infected and removed (or immune). On the other hand we allow higher spatial dimensions and also parameters depending on space and time. is last generalization is done to cope with possible abiotic effects as variations in temperature, humidity, wind velocity, carrier capacities, and so on; thus, the results... 

In this thesis, a model of predator-prey with a continuous threshold harvesting with refuge and without refuge the prey is formulated; and its dynamics, also, its direct effects on ecosystem such as the stability properties of some periodic solutions and coexistence eqilibria are surveyed. Numerical and theoretical analyses are used to investigate boundedness of solutions, stability of eqilibria, periodic orbits, bifurcations and heteroclinic orbits  

We revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it, employing methods familiar from super symmetric quantum mechanics. We also derive completeness and Riesz basis results for the associated root functions under less smoothness assumptions on the coefficients than usual, using operator theoretic methods only.After discussion about there topices, we need to know little about the functional analysis and partial differential equations. chapter one satisfied this aim.
 

In this study, Euler-Bernoulli and Timoshenko beams with delayed boundary control are investigated. Deriving governing dynamic feedback control equations, exponential stability of these beams are obtained under more generalized conditions. For this purpose, time delay of system is omitted using tools in control engineering; then, an appropriate control approachis is found for this modified system.In the next step,closed loop system is extracted, which demonstrate that system is stable exponentially. This stability which is acquired for closed loop systems is also valid for primary system