Results 61 to 70 of about 975 (193)
Lagrangian structures and multidimensional consistency [PDF]
, 2010 The conventional point of view is that the Lagrangian is a scalar object (or equivalently a volume form), which through the Euler-Lagrange equations provides us with one single equation (i.e., one per component of the dependent variable ...
Lobb, Sarah Beverley
core
Variational methods for problems from plasticity theory and for generalized Newtonian fluids [PDF]
, 1999 Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl ...
Seregin, G., +3 more
core +1 more source
On Compressible Fluid Flows of Forchheimer‐Type in Rotating Heterogeneous Porous Media
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of Forchheimer‐type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo‐pressure.
Emine Celik, Luan Hoang, Thinh Kieu
wiley +1 more source
On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
wiley +1 more source
Local and global well-posedness of SPDE with generalized coercivity conditions [PDF]
, 2013 In this paper we establish the local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions.
Röckner, Michael, Liu, Wei
core +1 more source
Nordgren PINNs to VQE: Advancing Hydraulic Fracturing Simulations in Shale Reservoirs
International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT This study advances hydraulic fracturing simulations in shale reservoirs using two computational paradigms, Physics‐Informed Neural Networks (PINNs) and the Variational Quantum Eigensolver (VQE). PINNs were employed to solve Nordgren's equation, which governs fracture width evolution, by embedding physical laws into the neural network ...
Dennis Delali Kwesi Wayo +7 more
wiley +1 more source
Approximate Reachability for Feedback Linearizable Systems
Optimal Control Applications and Methods, EarlyView.The backwards reachable set for a dynamical system is the set of states for which there exists a constraint admissible trajectory that reaches a given terminal set. Conventional grid‐based approaches for computing these sets are intractable for many applications.
Vincent Liu +2 more
wiley +1 more source
Concentrations of solutions to time-discretizied compressible Navier-Stokes equations [PDF]
, 2006 The compactness properties of solutions to time-discretization of compressible Navier-Stokes equations are investigated in three dimensions.
Sokolowski, Jan +1 more
core +2 more sources
Adaptive Sliding‐Mode Control of a Perturbed Diffusion Process With Pointwise In‐Domain Actuation
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT A sliding mode–based adaptive control law is proposed for a class of diffusion processes featuring a spatially‐varying uncertain diffusivity and equipped with several point‐wise actuators located at the two boundaries of the spatial domain as well as in its interior.
Paul Mayr +3 more
wiley +1 more source
Generalized gradient flow structure of internal energy driven phase field systems [PDF]
, 2015 In this paper we introduce a general abstract formulation of a variational thermomechanical model, by means of a unified derivation via a generalization of the principle of virtual powers for all the variables of the system, including the thermal one. In
Bonetti, Elena, Rocca, Elisabetta
core +1 more source