The present paper concerns with the global structure and asymptotic behavior of the discontinuous solutions to flood wave equations. By solving a free boundary problem, we first obtain the global structure and large time behavior of the weak solutions containing two shock waves. For the Cauchy problem with a class of initial data, we use Glimm scheme to obtain a uniform BV estimate both with re...

We present an exponentially convergent numerical method to approximate the solution of Cauchy problem for inhomogeneous fractional differential equation with unbounded operator coefficient and Caputo derivative in time. The is based on newly obtained formula that consolidates mild representations sub-parabolic, parabolic sub-hyperbolic equations sectorial $A$ non-zero initial data. involved int...

We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call this a subspace of stability. For more ge...

Abstract: The solution to problem of an orthotropic long cylinder subjected to torsional loading is first obtained by means of separation valuables. The cylinder is twisted by two lateral shear tractions and the ends of the cylinder surface of the cylinder are stress-free. First, the domain under consideration is weakened by an axisymmetric rotational Somigliana ring dislocation. The dislocatio...

The posterior moments of parameters specifying distributions are minimum mean square Bayesian estimators for the corresponding moments of those parameters, and as such are ubiquitous in the Bayesian approach to statistical inference of distributions. The Cauchy distribution is most notable for its wide tails, decided absence of high-order moments, and non-existence of less-than-data dimension s...

1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Full...