Results 41 to 50 of about 87,102,086 (248)

Nonnegative weak solutions of thin-film equations related to viscous flows in cylindrical geometries [PDF]

Journal of evolution equations (Printed ed.), 2019
Motivated by models for thin films coating cylinders in two physical cases proposed in Kerchman (J Fluid Mech 290:131–166, 1994) and Kerchman and Frenkel (Theor Comput Fluid Dyn 6:235–254, 1994), we analyze the dynamics of corresponding thin-film models.
J. Marzuola, Sterling Swygert, R. Taranets   +2 more
semanticscholar   +1 more source

Existence of $$C^\alpha $$ solutions to integro-PDEs [PDF]

Calculus of Variations and Partial Differential Equations, 2017
This paper is concerned with existence of a $C^{\alpha}$ viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to prove H\"older
Chenchen Mou
semanticscholar   +1 more source

Global Weak Solutions in a PDE-ODE System Modeling Multiscale Cancer Cell Invasion [PDF]

SIAM Journal on Mathematical Analysis, 2014
We prove the global existence, along with some basic boundedness properties, of weak solutions to a PDE-ODE system modeling the multiscale invasion of tumor cells through the surrounding tissue matrix. The model has been proposed in [G. Meral, C. Stinner, and C.
Christian Stinner, Christina Surulescu, Michael Winkler   +2 more
openaire   +3 more sources

Continuity equations and ODE flows with non-smooth velocity [PDF]

, 2014
In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this framework, we deal with velocity fields that are not smooth, but
Crippa, Gianluca, Ambrosio, Luigi
core   +1 more source

Conditional Symmetries and Riemann Invariants for Hyperbolic Systems of PDEs [PDF]

, 2007
This paper contains an analysis of rank-k solutions in terms of Riemann invariants, obtained from interrelations between two concepts, that of the symmetry reduction method and of the generalized method of characteristics for first order quasilinear ...
Huard, Benoit, Grundland, A. Michel
core   +1 more source

Weak solution of semi-linear PDE, BSDE and homogenization

Monte Carlo Methods and Applications, 2001
The author considers a semilinear PDE of the following type \[ \begin{cases}{\partial u^\varepsilon (t,x)\over \partial t}+L^\varepsilon u^\varepsilon (t,x)+ h\bigl(t,x/ \varepsilon,x,u^\varepsilon (t,x)\bigr)+\nabla u^\varepsilon (t,x)\widehat h\bigl(t,x/ \varepsilon,x, u^\varepsilon (t,x)\bigr) =0,\\ (t,x)\in[s,T] \times{\mathcal O},\\ u^\varepsilon ...
openaire   +5 more sources

Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness [PDF]

, 2019
In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation.
Hömberg, Dietmar Josef, Hömberg, Dietmar, Lasarzik, Robert   +2 more
core   +1 more source

Multiplicity of weak solutions in double phase Kirchhoff elliptic problems with Neumann conditions

Boundary Value Problems
In this paper, we investigate the existence of weak solutions for a class of double phase Kirchhoff elliptic problems under Neumann boundary conditions. The problem is characterized by the equation { − K 1 ( ∫ Λ A ( y , ∇ ζ ) d y ) div a ( y , ∇ ζ ) − K ...
Ahmed Ahmed, Mohamed Saad Bouh Elemine Vall, Salah Boulaaras   +2 more
doaj   +1 more source

On the second-order regularity of solutions to widely singular or degenerate elliptic equations [PDF]

Annali di Matematica Pura ed Applicata
We consider local weak solutions to PDEs of the type $$ -\,\textrm{div}\left( (\vert Du\vert -\lambda )_{+}^{p-1}\frac{Du}{\vert Du\vert }\right) =f\,\,\,\,\,\,\,\text {in}\,\,\Omega , $$ where ...
Pasquale Ambrosio, A. Grimaldi, Antonia Passarelli di Napoli   +2 more
semanticscholar   +1 more source

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

Journal of Differential Equations, 2018
In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network.
Jian-Guo Liu, Xiangsheng Xu
openaire   +3 more sources