Results 301 to 310 of about 159,157 (335)

On a class of second order Fuchsian hyperbolic equations

Annali di Matematica Pura ed Applicata, 1986
Let P be of the form: \[ (1)\quad P=-tD^ 2_ t+A(t,x,D_ y)+a(t,x)D_ t+b(t,x)D_ y+c(t,x), \] where: (i) the principal part of P; \(-tD\) \(2_ t+A(t,x,D_ y)\) is strictly hyperbolic for \(t>0.\) (ii) A(t,x,\(\cdot)\), b(t,x) and \(c(t,x)\in C^{\infty}(R_ t\times M)\), where M is a \(C^{\infty}\)-manifold without boundary. The aim of this paper is to solve
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Carleman Estimate for a General Second-Order Hyperbolic Equation

2020
In this article, we consider a general second-order hyperbolic equation. We first establish a modified Carleman estimate for this equation by adding some functions of adjustment. Then general conditions imposed on the principal parts, mixed with the weight function and the functions of adjustment are derived.
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The approximation of second-order hyperbolic differential-operator equations

USSR Computational Mathematics and Mathematical Physics, 1987
See the review in Zbl 0631.65085.
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Stabilization of statistical solutions of second-order hyperbolic equations

Russian Mathematical Surveys, 1984
The stabilization of statistical solutions of the Cauchy problem for general second order hyperbolic equations is investigated for initial data with zero average and finite average density of the energy and satisfying the so called condition for strong intermixture.
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General Initial-Boundary Problems for Second Order Hyperbolic Equations

1981
The general initial-boundary problem for a second order hyperbolic equation is considered for two classes of domains: domains with boundaries which are strictly concave with respect to the bicharacteristics of the hyperbolic operator and domains with boundaries strictly convex with respect to these bicharacteristics.
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Complex Analytic Method for Hyperbolic Equations of Second Order

1999
At first hyperbolic numbers and hyperbolic complex functions are introduced. On this basis existence and uniqueness of solutions of oblique derivative problems for some hyperbolic complex equations of second order are discussed by a complex analytic method.
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

DeepXDE: A Deep Learning Library for Solving Differential Equations

SIAM Review, 2021
Lu Lu, George E Karniadakis
exaly  

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

Computer Methods in Applied Mechanics and Engineering, 2020
Esteban Samaniego, Somdatta Goswami, Timon Rabczuk   +2 more
exaly  

New Creatinine- and Cystatin C–Based Equations to Estimate GFR without Race

New England Journal of Medicine, 2021
Lesley A Inker, Nwamaka D Eneanya, Josef Coresh   +2 more
exaly