Results 31 to 40 of about 14,444,000 (235)

Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

Boundary Value Problems, 2021
The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and the density of the operator range generated ...
Abdelkader Djerad, Ameur Memou, Ali Hameida   +2 more
doaj   +1 more source

Well-posedness of nonlinear Schrödinger equations from deterministic and probabilistic viewpoints [PDF]

In this thesis, we study the Cauchy problem for nonlinear Schrödinger equations (NLS) in various settings. Firstly, we consider NLS with a quadratic nonlinearity |u|² on the two-dimensional torus.
Liu, Ruoyuan
core   +1 more source

Explicit Methods for Inverse Source Identification in Transient Diffusion via Truncated Eigenfunction Regularization of Temperature Measurements

Heat Transfer, EarlyView.
ABSTRACT This work presents and compares two explicit approaches for estimating space‐ and time‐dependent source terms in parabolic diffusion equations, derived from analytical solutions obtained through the Classical Integral Transform Technique (CITT).
André J. P. de Oliveira, Diego C. Knupp, Luiz A. S. Abreu, Mousa J. Huntul, David A. Pelta, Antônio J. da Silva Neto   +5 more
wiley   +1 more source

Well-Posedness of the Boundary Layer Equations [PDF]

SIAM Journal on Mathematical Analysis, 2003
We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. Theproof is achieved applying the abstract Cauchy--Kowalewski theorem to the boundary layer equations once the ...
LOMBARDO, Maria Carmela, Cannone, M., SAMMARTINO, Marco Maria Luigi   +2 more
openaire   +3 more sources

Intrinsically Design‐Rule‐Compliant Nanophotonic Inverse Design via Learned Generative Manifolds

Laser &Photonics Reviews, EarlyView.
A generative reparameterization framework for nanophotonic inverse design is introduced, restricting optimization to a learned manifold of design‐rule‐compliant geometries. Unlike conventional penalty‐based approaches, fabrication constraints are encoded intrinsically within the design representation.
Bahrem Serhat Danis, Demet Baldan Desdemir, Enes Akcakoca, Zeynep Ipek Yanmaz, Gulzade Polat, Ahmet Onur Dasdemir, Aytug Aydogan, Abdullah Magden, Emir Salih Magden   +8 more
wiley   +1 more source

Well-posedness of a model for water waves with viscosity [PDF]

, 2012
The water wave equations of ideal free–surface fluid mechanics are a fundamental model of open ocean movements with a surprisingly subtle well–posedness theory.
David Ambrose (7936688), David Nicholls (1822744), Jerry Bona (7936691)   +2 more
core   +3 more sources

Low regularity well-posedness of the modified and the generalized Korteweg-de Vries equations [PDF]

, 2021
In this thesis, we study the well-posedness of the modified and generalized Korteweg-de Vries equations on the one-dimensional torus. We first consider the complex-valued modified Korteweg-de Vries equation (mKdV).
Chapouto, Andreia
core   +1 more source

A Kantorovich Version of Bernstein‐Type Logarithmic Operators

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, we introduce a Kantorovich version of the Bernstein‐type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that preserve exponential functions: here, the exponential weights are replaced by logarithmic ones and the corresponding operators preserve the logarithmic functions.
Laura Angeloni, Danilo Costarelli, Chiara Darielli   +2 more
wiley   +1 more source

Nonconstant Positive Steady States for a Predator–Prey System With Signal‐Dependent Diffusion

Mathematische Nachrichten, EarlyView.
ABSTRACT This paper investigates a highly nonlinear predator–prey reaction–diffusion system featuring signal‐dependent prey diffusion, where the motility of the prey is modulated by a chemical signal released by predators. For unbounded functional responses, we establish the global‐in‐time existence and uniform‐in‐time boundedness of classical ...
Qigang Deng, Hao Shen, Ranchao Wu, Hao Wang   +3 more
wiley   +1 more source

Levitin–Polyak Well Posedness for Fuzzy Optimization Problems Through a Linear Ordering

Mathematics
We propose a reformulated notion of Levitin–Polyak (abbreviated as LP) well posedness for fuzzy optimization problems formulated in the fuzzy order-preserving (FOP) setting, where minimizing sequences are governed by a total ordering defined on fuzzy ...
Rattanaporn Wangkeeree, Panatda Boonman, Nithirat Sisarat   +2 more
doaj   +1 more source