Abstract:
We study an initial-boundary value problem for a non-linear Sobolev equation
containing a summand non-local in time and an inhomogeneity. The equation
simulates unsteady processes in semiconductors. We find sufficient conditions
for the unique solubility of the problem, both global in time and local (rather
than global). In the case when the problem is soluble only locally, we find
upper and lower bounds for the lifespan of a solution.
Keywords:equations of Sobolev type, blow-up of solutions, method of energy estimates.
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