scholarly journals Well-posed results for nonlocal biparabolic equation with linear and nonlinear source terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Le Dinh Long ◽  
Ho Duy Binh ◽  
Kim Van Ho Thi ◽  
Van Thinh Nguyen
Keyword(s):  
Mild Solution ◽  
Source Term ◽  
Nonlocal Conditions ◽  
Regularity Property ◽  
Banach Fixed Point Theorem ◽  
Source Terms ◽  
Nonlinear Source ◽  
First Results ◽  
Linear And Nonlinear ◽  
Well Posed

AbstractIn this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity property of the mild solution for the linear source term while we apply the Banach fixed-point theorem to study the existence and uniqueness of the mild solution for the nonlinear source term. In both cases, we show that the mild solution of our problem converges to the solution of an initial value problem as the parameter epsilon tends to zero. The novelty in our study can be considered as one of the first results on biparabolic equations with nonlocal conditions.

scholarly journals Determination of a nonlinear source term in a diffusion equation with final observations

2004 ◽  
Vol 2004 (14) ◽  
pp. 741-753 ◽  
Author(s):  
Gongsheng Li ◽  
Yichen Ma ◽  
Kaitai Li
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Integral Identity ◽  
Source Term ◽  
Conditional Stability ◽  
Inverse Source Problem ◽  
Source Terms ◽  
Nonlinear Source ◽  
Quasilinear Diffusion

This paper deals with an inverse problem of determining a nonlinear source term in a quasilinear diffusion equation with overposed final observations. Applying integral identity methods, data compatibilities are deduced by which the inverse source problem here is proved to be reasonable and solvable. Furthermore, with the aid of an integral identity that connects the unknown source terms with the known data, a conditional stability is established.

scholarly journals On The Initial Value Problem For Fractional Volterra Integrodifferential Equations With A Caputo - Fabrizio Derivative

2021 ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Nguyen Anh Tuan ◽  
Donal O’regan ◽  
Vo Viet Tri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Source Term ◽  
Main Tool ◽  
Integrodifferential Equations ◽  
Banach Fixed Point Theorem ◽  
Initial Value ◽  
Locally Lipschitz ◽  
Source Case ◽  
Well Posed

In this paper, time fractional integrodifferential equations with the Caputo - Fabrizio type derivative will be considered. In the case of a globally Lipschitz source term we obtain a global well - posed result on $\R^N$ for our problem. For the locally Lipschitz source case, we present existence and uniqueness and a finite time blow result for the solution. Our main tool is the Banach fixed point theorem and we extend  a  recent  paper of N.H. Tuan and Y. Zhou.

scholarly journals CP-violating transport theory for electroweak baryogenesis with thermal corrections

2021 ◽  
Vol 2021 (11) ◽  
pp. 042
Author(s):  
Kimmo Kainulainen
Keyword(s):  
Source Term ◽  
Transport Theory ◽  
Finite Width ◽  
Source Terms ◽  
Boltzmann Equations ◽  
Current Divergence ◽  
The One ◽  
Infrared Divergences ◽  
Correct Implementation ◽  
Divergence Equations

Abstract We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences. We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.

scholarly journals Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Tianlong Shen ◽  
Jianhua Huang ◽  
Jin Li
Keyword(s):  
Fixed Point ◽  
Diffusion Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Banach Fixed Point Theorem ◽  
Fractional Operator ◽  
Initial Value ◽  
Delayed Reaction

The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.

Sign in / Sign up

Export Citation Format

Share Document