Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data

Extinction for Fast Diffusion Equations with Nonlinear Sources

We establish conditions for the extinction of solutions, in finite time, of the fast diffusion problem ut = ∆um +λup, 0 < m < 1, in a bounded domain of RN with N > 2. More precisely, we show that if p > m, the solution with small initial data vanishes in finite time, and if p < m, the maximal solution is positive for all t > 0. If p = m, then first eigenvalue of the Dirichlet problem plays a role.

Reaction-diffusion equations with nonlinear boundary conditions in narrow domains

Second initial boundary problem in narrow domains of width ǫ ≪ 1 for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution of such a problem converges as ǫ ↓ 0 to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some r...

Lyapunov functionals for boundary-driven nonlinear drift–diffusion equations

We exhibit a large class of Lyapunov functionals for nonlinear drift–diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic manyparticle systems, the zero-range process and the Ginzburg–Landau dynamics, which we describe briefly. We prove, as an application, linear inequalities between such an en...

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...