Inhomogeneous boundary value problems for the von Kármán equations. II
Inhomogeneous boundary value problems for the von Kármán equations. I
Inhomogeneous Fractional Diffusion Equations
2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analytic solution can be written...
Inhomogeneous Gevrey ultradistributions and Cauchy problem
Inhomogeneous parabolic Neumann problems
Second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions are studied. Existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder are proved using methods from the theory of integrated semigroups, showing in particular the well-posedness of the abstract Cauchy problem in spaces of continuous functions. Under natural assumptions on the coefficients and the inhomogeneity the...
Initial and Boundary Value Problems for Functional Differential Equations via the Topological Transversality Method: A Survey
Initial and boundary value problems for partial functional differential equations.
Initial boundary value problem for a system in elastodynamics with viscosity.
Initial boundary value problem for generalized Zakharov equations
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Initial boundary value problems of the Degasperis-Procesi equation
We mainly study initial boundary value problems for the Degasperis-Procesi equation on the half line and on a compact interval. By the symmetry of the equation, we can convert these boundary value problems into Cauchy problems on the line and on the circle, respectively. Applying thus known results for the equation on the line and on the circle, we first obtain the local well-posedness of the initial boundary value problems. Then we present some blow-up and global existence results for strong solutions....
Initial limits of temperatures on arbitrary open sets.
Initial measures for the stochastic heat equation
We consider a family of nonlinear stochastic heat equations of the form , where denotes space–time white noise, the generator of a symmetric Lévy process on , and is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that for some , we prove that if is a finite measure of compact support, then the solution is...
Initial traces of solutions to a one-phase Stefan problem in an infinite strip.
The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1) ut - Δ(u - 1)+ = 0, in D'(Rn x (0,T)),for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2) ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C, 0 <...
Initial value problems in elasticity
Initial Value Problems in Lp for Systems with Variable Coefficients.
Initial-boundary value problem for equations of generalized Newtonian incompressible fluid.
Initial-boundary value problem for generalized Stokes equations
The paper is concerned with the solvability theory of the generalized Stokes equations arising in the study of the motion of non-Newtonian fluids.
Initial-boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermodiffusion in solid body.
Initial-boundary value problem for the discrete Boltzmann equation