Nonlocal problem with impulse action for parabolic equations of vector order
Abstract
UDC 517.956.4
For $\{\overrightarrow{p};\overrightarrow{h}\}$-parabolic equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered.
This condition linearly combines the values of the solution at the initial and an intermediate points in time.
The conditions for the correct solvability of this problem are clarified and the formula for its solution is found.
With the help of the obtained results, the corresponding problem with impulse action is solved.
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