Convergence to equilibrium for some nonlinear evolution equations with dynamical boundary condition

Convergence to equilibrium for some nonlinear evolution equations with dynamical boundary condition

The asymptotic behavior of global solutions of nonlinear evolution equations, in particular convergence to a certain equilibrium as time tends to infinity has become one of the main concerns in the field of nonlinear evolution equations since 1980s. For one space dimension case, significant progresses have been made (see e.g., [6]). However, the situation in higher space dimension case is much ...

Convergence to a Positive Equilibrium for Some Nonlinear Evolution Equations in a Ball

(1.1)P ut −∆u = f(u) in R × Ω; u = 0 on R × ∂Ω where f ∈ C(R) generates a local semi-flow on H 0 (Ω)∩L∞(Ω). If u : R×Ω→ R is a global bounded solution of (1.1)P , then due to the energy dissipation, and as a consequence of LaSalle’s invariance principle, the ω-limit set ω(u) of u consists of stationary solutions only: in particular, as t→ +∞, u(t, x) approaches the set of solutions of the ellip...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces

This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.