On the existence of weak solutions for a semilinear singular hiperbolic system.
In this paper we prove the existence of a weak solution for a given semilinear singular real hyperbolic system.
On the existence of weak solutions for -Laplacian systems with weights.
On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures.
On the exponential growth of solutions to nonlinear hyperbolic equations.
On the exterior Dirichlet problem for
On the extinction of the solution for an elliptic equation in a cylindrical domain
On the Fejér-F. Riesz inequality in
On the First Eigenvalue of Non-Uniformly Elliptic Boundary Value Problems.
On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion
Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of smooth-front...
On the -convergence of Morrey operators
Following Morrey [14] we associate to any measurable symmetric matrix valued function such that
On the generalized Fourier transforms associated with Schrödinger operators with long-range perturbations.
On the Generalized Korteweg-De Vries Equation.
On the Gevrey analyticity of solutions of semilinear perturbations of powers of the Mizohata operator.
On the Ginzburg-Landau energy with weight
On the global attractors for a class of semilinear degenerate parabolic equations
We prove the existence and upper semicontinuity with respect to the nonlinearity and the diffusion coefficient of global attractors for a class of semilinear degenerate parabolic equations in an arbitrary domain.
On the global existence for the axisymmetric Euler equations
This paper deals with the global well-posedness of the D axisymmetric Euler equations for initial data lying in critical Besov spaces . In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity .
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...
On the global regularity of -dimensional generalized Boussinesq system
We study the -dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.
On the global regularity of subcritical Euler–Poisson equations with pressure
We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual -law pressure, , admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the -system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann...
On the global well-posedness of the Boussinesq system with zero viscosity
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.