Regularity of a inverse problem for generic parabolic equations

The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary value inputs.Comment: 9 page

On prescribed change of profile for solutions of parabolic equations

Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that this problem is well-posed in L_2-setting. Existence and regularity results are established, as well as an analog of the maximum principle

Opportunities and prospects for non-seismic methods to search for hydrocarbon accumulations and the geosoliton concept of their formation

Geosolitonic concept of hydrocarbon deposits formation allows to elaborate efficient methods of conducting complex geophysical studies capable to guarantee successful prospecting and exploration of oil and gas deposits with complex structure, controlled by geosolitonic mechanism of the Earth degassing. The main showings of HC deposits within the limits of this concept are geosolitonic pipes and vortical character of physical fields displayed in the materials of seismic exploration, electrical survey, MTS, in gravity and magnetic fields. For solving non-correct problems of geophysics (gravimetry, magnetometry, electrical survey) because of their limited selections robust methods of processing and interpretation are applied based on regulation, optimal filtration and introcontinuation of geo-fields in the area variant. The most general and promising approach of the theory of geopotential fields interpretation is the direction of equivalent redistributions: sweeping-out of masses, according to Poincaree from the area abroad, realized by A. V. Ovcha-renko, sweeping-out from the area to area, swelling, according to V. S. Lee and concentration of masses-sources according to D. Zidarov and V. G. Filatov in two-dimensional and three-dimensional statement of Yu.V. Glasko. The concept of geosolitonic degassing of the Earth has been practically tested in the West Siberia. The method of conducting complex geophysical studies elaborated on its base improved the effectiveness of prospecting and exploration of oil and gas deposits