scholarly journals Optimal existence and uniqueness theory for the fractional heat equation

2017 ◽  
Vol 153 ◽  
pp. 142-168 ◽  
Author(s):  
Matteo Bonforte ◽  
Yannick Sire ◽  
Juan Luis Vázquez
Keyword(s):  
Heat Equation ◽  
Existence And Uniqueness ◽  
Fractional Heat Equation ◽  
Uniqueness Theory

scholarly journals Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Dengfeng Xia ◽  
Litan Yan ◽  
Weiyin Fei
Keyword(s):  
Fixed Point ◽  
Heat Equation ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Fractional Laplacian ◽  
Brownian Sheet ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Fixed Point Principle ◽  
Uniqueness Of The Solution

We consider the stochastic heat equation of the form∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H,whereW˙His the fractional noise,L˙is a (pure jump) Lévy space-time white noise,Δis Laplacian, andΔα=-(-Δ)α/2is the fractional Laplacian generator onR, andf,σ:[0,T]×R×R→Rare measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.

scholarly journals Existence and uniqueness regions for solutions of nonlinear equations

1978 ◽  
Vol 19 (2) ◽  
pp. 277-282 ◽  
Author(s):  
A.L. Andrew
Keyword(s):  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Kantorovich Theorem ◽  
Potential Applications ◽  
Uniqueness Theory

A refinement of the Newton-Kantorovich Theorem, which has many-potential applications in existence - uniqueness theory, is used to strengthen a result of Lancaster and Rokne concerning existence and uniqueness regions for zeros of operator polynomials.

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

scholarly journals CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP

2010 ◽  
Vol 13 (07) ◽  
pp. 1103-1129 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ANNE EYRAUD-LOISEL
Keyword(s):  
Credit Risk ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Risk Premia ◽  
Contingent Claims ◽  
Quadratic Growth ◽  
Utility Preferences ◽  
Random Times ◽  
Uniqueness Theory

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

scholarly journals No local L1 solutions for semilinear fractional heat equations

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Kexue Li
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Heat Equations ◽  
Fractional Heat Equation ◽  
The Cauchy Problem

AbstractWe study the Cauchy problem for the semilinear fractional heat equation

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