We consider doubly nonlinear anisotropic degenerate parabolic equations, supplemented with an initial condition and a homogeneous Dirichlet boundary condition. We introduce a notion of entropy solution and prove that the entropy solution is uniquely determined by its data.

We consider test strings and test branes ending on Dp-branes (p ≤ 6) and NS5-branes in the background, for a heuristic understanding of the dynamics. Whenever some supersymmetry is preserved, a simple BPS bound appears, but the central charge in question is measured by certain isotropic coordinate system, rather than by the actual spacetime geometry. This way, the ground state energy is indepen...

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

We provide a polynomial decay rate for the energy of the wave equation with a dissipative boundary condition in a cylindrical trapped domain. A new kind of interpolation estimate for the wave equation with mixed Dirichlet-Neumann boundary condition is established from a construction based on a Fourier integral operator involving a good choice of weight functions.

In this paper we provide‎ ‎existence results for positive solution to‎ ‎Dirichlet p(t)-Laplacian boundary value problems‎. ‎The sublinear and‎ ‎superlinear cases are considerd‎.

Consider the semilinear heat equation ∂tu = ∂ xu + λσ(u)ξ on the interval [0 , 1] with Dirichlet zero boundary condition and a nice nonrandom initial function, where the forcing ξ is space-time white noise and λ > 0 denotes the level of the noise. We show that, when the solution is intermittent [that is, when infz |σ(z)/z| > 0], the expected L-energy of the solution grows at least as exp{cλ} an...

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

We prove sharp convergence rates for a class of domain embedding methods for elliptic boundary value problems. The theory is established for Dirichlet, Neumann, and Robin boundary conditions, and is unified in a new formulation for mixed boundary condition. On the continuous level, the methods for these boundary value problems perform equally well.

We consider test strings and test branes ending on Dp-branes (p ≤ 6) and NS5-branes in the background, for a heuristic understanding of the dynamics. Whenever some supersymmetry is preserved, a simple BPS bound appears, but the central charge in question is measured by certain isotropic coordinate system, rather than by the actual spacetime geometry. This way, the ground state energy is indepen...

The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.