Results 11 to 20 of about 2,990 (216)

Quasilinear parabolic systems

Journal of Differential Equations, 1976
AbstractParabolic systems of partial differential equations are developed and applications are discussed. The systems are quasilinear in divergence form with high-order coefficient matrices which are neither symmetric nor sparse. Weak existence, uniqueness, and stability are established for an appropriate initial-boundary value problem.
Cannon, John R., Ford, Wayne T., Lair, Alan V.   +2 more
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Global solutions for quasilinear parabolic systems

Journal of Differential Equations, 2004
An approach is presented for proving the global existence of classical solutions of the quasilinear parabolic systems like \[ u_t-\text{ div}(a(t,x,u,v)\nabla u)=f(t,u,v,\nabla u), \quad t>0, \] \[ v_t-\alpha\,\text{ div}(b(t,x,v)\nabla v)=g(t,u,v,\alpha\nabla v), \quad t>0, \] with homogeneous Dirichlet boundary condition in bounded domain with smooth
Constantin, Adrian, Escher, Joachim, Yin, Zhaoyang   +2 more
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On the local integrability and boundedness of solutions to quasilinear parabolic systems

Electronic Journal of Qualitative Theory of Differential Equations, 2004
We introduce a structure condition of parabolic type, which allows for the generalization to quasilinear parabolic systems of the known results of integrability, and boundedness of local solutions to singular and degenerate quasilinear parabolic ...
T. Giorgi, M. O'Leary
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Nontrivial solutions for resonance quasilinear elliptic systems [PDF]

Advances in Nonlinear Analysis
We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically (p,q)\left(p,q)-linear at infinity.
Borgia Natalino, Cingolani Silvia, Vannella Giuseppina   +2 more
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Lyapunov-type inequalities for n-dimensional quasilinear systems

Electronic Journal of Differential Equations, 2013
In this article, inspired by the paper of Yang et al [12], we establish new versions of Lyapunov-type inequalities for a certain class of Dirichlet quasilinear systems.
Mustafa Fahri Aktas
doaj   +1 more source

Application of linear electron Bernstein current drive models in reactor-relevant spherical tokamaks

Nuclear Fusion, 2023
Electron Bernstein current drive (EBCD) systems in spherical tokamaks are sensitive to plasma and launch conditions, and therefore require large parametric scans to optimise their design.
Bodhi Biswas, David Speirs, Simon Freethy, Roddy Vann   +3 more
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On Some Quasilinear Systems

Rocky Mountain Journal of Mathematics, 1997
The authors consider the Dirichlet problem for the quasilinear system \[ -\Delta_p u = F_u(u,v), \quad\Delta_q v = F_v(u,v), \quad \text{in} \Omega, \qquad u = v = 0, \quad \text{on} \partial \Omega, \tag{P} \] on a given bounded domain \(\Omega\subset \mathbb{R}^N\) with smooth boundary, where \(N>2 ...
Peral, I., Vorst, R.C.A.M. van der
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Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems [PDF]

, 2006
We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, $-\sum_{\alpha=1}^d \partial_{x_\alpha ...
Suli, Endre, Christoph Ortner, Süli, E, Endre Süli, Ortner, Christoph, Ortner, C   +5 more
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An Eigenvalue Problem for Quasilinear Systems

Rocky Mountain Journal of Mathematics, 2007
This paper deals with the existence of positive solutions for the \(n\)-dimensional quasilinear system \[ ({\mathbf \Phi}({\mathbf u}'))' + \lambda {\mathbf h}(t) {\mathbf f}({\mathbf u}) = 0, \quad 0 < t < 1 \] with the boundary condition \({\mathbf u}(0)={\mathbf u}(1)=0\), where \({\mathbf u}=(u_1,\dots,u_n)\), \({\mathbf \Phi}({\mathbf u ...
Henderson, Johnny, Wang, Haiyan
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Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems

Boundary Value Problems, 2018
This paper is concerned with the existence of ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems in R3 $\mathbb {R}^{3}$ which have appeared in plasma physics, as well as in the description of high-power ultrashort ...
Liejun Shen
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