Partial Differential Equations and Analytic Continuations

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...

The Analytic Theory of Systems of Partial Differential Equations

Continuations and Functional Equations

The first part of this writeup gives Riemann’s argument that the completion of zeta, Z(s) = π−s/2Γ(s/2)ζ(s), Re(s) > 1 has a meromorphic continuation to the full s-plane, analytic except for simple poles at s = 0 and s = 1, and the continuation satisfies the functional equation Z(s) = Z(1− s), s ∈ C. The continuation is no longer defined by the sum. Instead, it is defined by a wellbehaved integ...

Continuations and Functional Equations

The first part of this writeup gives Riemann’s argument that the completion of zeta, Z(s) = π−s/2Γ(s/2)ζ(s), Re(s) > 1 has a meromorphic continuation to the full s-plane, analytic except for simple poles at s = 0 and s = 1, and the continuation satisfies the functional equation Z(s) = Z(1− s), s ∈ C. The continuation is no longer defined by the sum. Instead, it is defined by a wellbehaved integ...

Continuations and Functional Equations

The first part of this writeup gives Riemann’s argument that the completion of zeta, Z(s) = π−s/2Γ(s/2)ζ(s), Re(s) > 1 has a meromorphic continuation to the full s-plane, analytic except for simple poles at s = 0 and s = 1, and the continuation satisfies the functional equation Z(s) = Z(1− s), s ∈ C. The continuation is no longer defined by the sum. Instead, it is defined by a wellbehaved integ...