Existence and Uniqueness Theorem for a Class of Singular Nonlinear Partial Differential Equations | Zendy

Dennis B. Bacani | Zendy; Hidetoshi Tahara | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Existence and Uniqueness Theorem for a Class of Singular Nonlinear Partial Differential Equations

Author(s) -

Dennis B. Bacani,

Hidetoshi Tahara

Publication year - 2012

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/90

Subject(s) - mathematics , uniqueness , class (philosophy) , nonlinear system , picard–lindelöf theorem , mathematical analysis , partial differential equation , singular solution , fixed point theorem , artificial intelligence , computer science , physics , quantum mechanics

This paper deals with singular nonlinear partial differential equations of the form t∂u/∂t = F (t, x, u, ∂u/∂x), with independent variables (t, x) ∈ R × C, and where F (t, x, u, v) is a function continuous in t and holomorphic in the other variables. Using the Banach fixed point theorem, we show that a unique solution u(t, x) exists under the condition that F (0, x, 0, 0) = 0, Fu(0, x, 0, 0) = 0 and Fv(0, x, 0, 0) = x γ(x) with Re γ(0) < 0. 2010 Mathematics Subject Classification: Primary 35A01; Secondary 35A10, 35A20, 35F20.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research